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Hot questions in Differential Equations
1
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0
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1
TIFR ECE 2021 | Question: 4
The first-order differential equation $\frac{d y(t)}{d t}+2 y(t)=x(t)$ describes a particular continuous-time system initially at rest at origin i.e., $x(0)=0$. Consider the following statements? System is memoryless. System is causal. System is stable. Which of the ... correct. All $(1), (2)$ and $(3)$ are correct. Only $(2)$ and $(3)$ are correct. None of the above
The first-order differential equation $\frac{d y(t)}{d t}+2 y(t)=x(t)$ describes a particular continuous-time system initially at rest at origin i.e., $x(0)=0$. Consider ...
admin
46.4k
points
108
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admin
asked
Nov 30, 2022
Differential Equations
tifrece2021
differential-equations
first-order-differential-equation
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–
1
votes
0
answers
2
GATE ECE 2009 | Question: 1
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is $1$ $2$ $3$ $4$
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is$1$$2$$3$$4$
admin
46.4k
points
207
views
admin
asked
Sep 15, 2022
Differential Equations
gate2009-ec
differential-equations
second-order-differential-equation
+
–
1
votes
0
answers
3
GATE ECE 2010 | Question: 30
Consider a differential equation $\dfrac{d y(x)}{d x}-y(x)=x$ with the initial condition $y(0)=0$. Using Euler's first order method with a step size of $0.1$, the value of $y(0.3)$ is $0.01$ $0.031$ $0.0631$ $0.1$
Consider a differential equation $\dfrac{d y(x)}{d x}-y(x)=x$ with the initial condition $y(0)=0$. Using Euler's first order method with a step size of $0.1$, the value o...
admin
46.4k
points
36
views
admin
asked
Sep 15, 2022
Differential Equations
gate2010-ec
differential-equations
first-order-differential-equation
+
–
1
votes
0
answers
4
GATE ECE 2010 | Question: 3
A function $n(x)$ satisfies the differential equation $\frac{d^{2} n(x)}{d x^{2}}-\frac{n(x)}{L^{2}}=0$ where $L$ is a constant. The boundary conditions are: $n(0)=K$ and $n(\infty)=0$. The solution to this equation is $n(x)=K \exp (x / L)$ $n(x)=K \exp (-x / \sqrt{L})$ $n(x)=K^{2} \exp (-x / L)$ $n(x)=K \exp (-x / L)$
A function $n(x)$ satisfies the differential equation $\frac{d^{2} n(x)}{d x^{2}}-\frac{n(x)}{L^{2}}=0$ where $L$ is a constant. The boundary conditions are: $n(0)=K$ and...
admin
46.4k
points
36
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admin
asked
Sep 15, 2022
Differential Equations
gate2010-ec
differential-equations
second-order-differential-equation
+
–
1
votes
0
answers
5
GATE ECE 2011 | Question: 25
The solution of the differential equation $\frac{d y}{d x}=k y, y(0)=c$ is $x=c e^{-k y}$ $x=k e^{c y}$ $y=c e^{k x}$ $y=c e^{-k x}$
The solution of the differential equation $\frac{d y}{d x}=k y, y(0)=c$ is$x=c e^{-k y}$$x=k e^{c y}$$y=c e^{k x}$$y=c e^{-k x}$
admin
46.4k
points
107
views
admin
asked
Sep 3, 2022
Differential Equations
gate2011-ec
differential-equations
first-order-differential-equation
+
–
1
votes
0
answers
6
GATE ECE 2021 | Question: 2
Consider the differential equation given below. $\frac{dy}{dx}+\frac{x}{1-x^{2}}y=x\sqrt{y}$ The integrating factor of the differential equation is $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
Consider the differential equation given below.$$\frac{dy}{dx}+\frac{x}{1-x^{2}}y=x\sqrt{y}$$The integrating factor of the differential equation is$\left ( 1-x^{2} \right...
Arjun
6.5k
points
242
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Arjun
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Feb 19, 2021
Differential Equations
gateec-2021
differential-equations
first-order-differential-equation
+
–
0
votes
0
answers
7
GATE ECE 2020 | Question: 4
The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}-6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is $y=C_{1}e^{3x}+C_{2}e^{-3x}$ $y=(C_{1}+C_{2}x)e^{-3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=C_{1}e^{3x}$
The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}-6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is$y=C_{1}e^{3x}+C_{2}e^{-3x}$$y=(C_{1}+C_{2}x)e^{-3x}$$y=(C...
go_editor
1.9k
points
213
views
go_editor
asked
Feb 13, 2020
Differential Equations
gate2020-ec
differential-equations
second-order-differential-equation
+
–
0
votes
0
answers
8
GATE ECE 2020 | Question: 27
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y-1 \right )x?$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=-1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=-1$
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y-1 \right )x?$$\ln\mid y-1 \mid=0.5x^{...
go_editor
1.9k
points
119
views
go_editor
asked
Feb 13, 2020
Differential Equations
gate2020-ec
differential-equations
+
–
0
votes
0
answers
9
GATE ECE 2019 | Question: 2
The families of curves represented by the solution of the equation $\frac{dy}{dx}=\: – \left(\frac{x}{y} \right)^n$ for $n=-1$ and $n= +1,$ respectively, are Parabolas and Circles Circles and Hyperbolas Hyperbolas and Circles Hyperbolas and Parabolas
The families of curves represented by the solution of the equation$$\frac{dy}{dx}=\: – \left(\frac{x}{y} \right)^n$$for $n=-1$ and $n= +1,$ respectively, areParabolas a...
Arjun
6.5k
points
158
views
Arjun
asked
Feb 12, 2019
Differential Equations
gate2019-ec
differential-equations
+
–
0
votes
0
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10
GATE ECE 2019 | Question: 43
Consider the homogenous ordinary differential equation $x^{2}\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}+3y=0, \quad x>0$ with $y(x)$ as a general solution. Given that $y(1)=1 \quad \text{and} \quad y(2)=14$ the value of $y(1.5),$ rounded off to two decimal places, is________.
Consider the homogenous ordinary differential equation$$x^{2}\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}+3y=0, \quad x>0$$with $y(x)$ as a general solution. Given that$$y(1)=1 ...
Arjun
6.5k
points
146
views
Arjun
asked
Feb 12, 2019
Differential Equations
gate2019-ec
numerical-answers
differential-equations
engineering-mathematics
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–
0
votes
0
answers
11
GATE ECE 2015 Set 3 | Question: 28
Consider the differential equation $\dfrac{\mathrm{d^{2}}x(t) }{\mathrm{d} t^{2}} +3\frac{\mathrm{d}x(t)}{\mathrm{d} t} + 2x(t) = 0. $ Given $x(0) = 20$ and $x(1) = 10/e,$ where $e = 2.718,$ the value of $x(2)$ is ________.
Consider the differential equation$$\dfrac{\mathrm{d^{2}}x(t) }{\mathrm{d} t^{2}} +3\frac{\mathrm{d}x(t)}{\mathrm{d} t} + 2x(t) = 0. $$Given $x(0) = 20$ and $x(1) = 10/e,...
Milicevic3306
16.0k
points
195
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-3
numerical-answers
differential-equations
+
–
0
votes
0
answers
12
GATE ECE 2016 Set 3 | Question: 26
The particular solution of the initial value problem given below is $\frac{d^2y}{dx^2}+12\frac{dy}{dx}+36y=0\hspace{0.3cm} \text{ with } \hspace{0.3cm}y(0)=3\hspace{0.3cm} \text{ and }\hspace{0.3cm} \frac{dy}{dx} \bigg| _{x=0} =-36$ $(3-18x)e^{-6x}$ $(3+25x)e^{-6x}$ $(3+20x)e^{-6x}$ $(3-12x)e^{-6x}$
The particular solution of the initial value problem given below is$$\frac{d^2y}{dx^2}+12\frac{dy}{dx}+36y=0\hspace{0.3cm} \text{ with } \hspace{0.3cm}y(0)=3\hspace{0.3cm...
Milicevic3306
16.0k
points
102
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Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2016-ec-3
differential-equations
+
–
0
votes
0
answers
13
GATE ECE 2016 Set 2 | Question: 19
The response of the system $G(s)=\frac{s-2}{(s+1)(s+3)}$ to the unit step input $u(t)$ is $y(t)$. The value of $\frac{dy}{dt}$ at $t=0^{+}$ is _________
The response of the system $G(s)=\frac{s-2}{(s+1)(s+3)}$ to the unit step input $u(t)$ is $y(t)$. The value of $\frac{dy}{dt}$ at $t=0^{+}$ is _________
Milicevic3306
16.0k
points
83
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Milicevic3306
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Mar 27, 2018
Differential Equations
gate2016-ec-2
numerical-answers
differential-equations
+
–
0
votes
0
answers
14
GATE ECE 2015 Set 1 | Question: 25
The solution of the differential equation $\frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y=0$ with $y(0)=y’(0)=1$ is $(2-t)e^t$ $(1+2t)e^{-t}$ $(2+t)e^{-t}$ $(1-2t)e^t$
The solution of the differential equation $\frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y=0$ with $y(0)=y’(0)=1$ is$(2-t)e^t$$(1+2t)e^{-t}$$(2+t)e^{-t}$$(1-2t)e^t$
Milicevic3306
16.0k
points
73
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-1
differential-equations
+
–
0
votes
0
answers
15
GATE ECE 2015 Set 2 | Question: 26
Consider the differential equation $\dfrac{\mathrm{d} x }{\mathrm{d} t} = 10 – 0.2x$ with initial condition $x(0) = 1$. The response $x(t)$ for $t>0$ is $2-e^{-0.2t}$ $2-e^{0.2t}$ $50-49e^{-0.2t}$ $50-49e^{0.2t}$
Consider the differential equation $\dfrac{\mathrm{d} x }{\mathrm{d} t} = 10 – 0.2x$ with initial condition $x(0) = 1$. The response $x(t)$ for $t>0$ is$2-e^{-0.2t}$$2-...
Milicevic3306
16.0k
points
69
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Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-2
differential-equations
+
–
0
votes
0
answers
16
GATE ECE 2015 Set 2 | Question: 4
The general solution of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x} = \dfrac{1+\cos 2y}{1-\cos 2x}$ is $ \tan y – \cot x = c\:\text{(c is a constant)}$ $\tan x – \cot y = c\:\text{(c is a constant)}$ $\tan y + \cot x = c\:\text{(c is a constant)}$ $\tan x + \cot y = c\:\text{(c is a constant)}$
The general solution of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x} = \dfrac{1+\cos 2y}{1-\cos 2x}$ is$ \tan y – \cot x = c\:\text{(c is a constant)}...
Milicevic3306
16.0k
points
66
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Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-2
differential-equations
+
–
0
votes
0
answers
17
GATE ECE 2016 Set 2 | Question: 26
The ordinary differential equation $\frac{dx}{dt}=-3x+2, \text{ with }x(0) = 1$ is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is _________
The ordinary differential equation $$\frac{dx}{dt}=-3x+2, \text{ with }x(0) = 1$$ is to be solved using the forward Euler method. The largest time step that can be used t...
Milicevic3306
16.0k
points
65
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2016-ec-2
numerical-answers
differential-equations
+
–
0
votes
0
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18
GATE ECE 2014 Set 3 | Question: 5
If $z= xy \text{ ln} (xy)$, then $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}= 0 \\$ $y\frac{\partial z}{\partial x}= x\frac{\partial z}{\partial y} \\$ $x\frac{\partial z}{\partial x}= y\frac{\partial z}{\partial y} \\$ $y\frac{\partial z}{\partial x}+x\frac{\partial z}{\partial y}= 0$
If $z= xy \text{ ln} (xy)$, then$x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}= 0 \\$$y\frac{\partial z}{\partial x}= x\frac{\partial z}{\partial y} \\$$x...
Milicevic3306
16.0k
points
117
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-3
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
19
GATE ECE 2014 Set 1 | Question: 45
A system is described by the following differential equation, where $u(t)$ is the input to the system and $y(t)$ is the output of the system. $y(t) + 5y(t) = u(t)$ When $y(0) = 1$ and $u(t)$ is a unit step function, $y(t)$ is $0.2 + 0.8e^{-5t}$ $0.2 - 0.2e^{-5t}$ $0.8 + 0.2e^{-5t}$ $0.8 - 0.8e^{-5t}$
A system is described by the following differential equation, where $u(t)$ is the input to the system and $y(t)$ is the output of the system.$$y(t) + 5y(t) = u(t)$$When $...
Milicevic3306
16.0k
points
106
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2014-ec-1
differential-equations
+
–
0
votes
0
answers
20
GATE ECE 2013 | Question: 36
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$ Let $x(t)$ be a rectangular pulse given by $x(t) = \begin{cases} 1&0<t<2 \\ 0&\text{otherwise} \end{cases}$ ... $\frac{e^{-2s}}{(s+2)(s+3)} \\$ $\frac{1-e^{-2s}}{s(s+2)(s+3)} $
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$Let $x(t)$ be a rectangul...
Milicevic3306
16.0k
points
110
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2013-ec
differential-equations
laplace-transform
+
–
0
votes
0
answers
21
GATE ECE 2014 Set 3 | Question: 2
Which $ONE$ of the following is a linear non-homogeneous differential equation, where $x$ and $y$ are the independent and dependent variables respectively? $\frac{dy}{dx}+xy= e^{-x}$ $\frac{dy}{dx}+xy= 0$ $\frac{dy}{dx}+xy= e^{-y}$ $\frac{dy}{dx}+ e^{-y}= 0$
Which $ONE$ of the following is a linear non-homogeneous differential equation, where $x$ and $y$ are the independent and dependent variables respectively?$\frac{dy}{dx}+...
Milicevic3306
16.0k
points
104
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-3
differential-equations
+
–
0
votes
0
answers
22
GATE ECE 2013 | Question: 37
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing function is $x(t)$ and the initial condition is $y(0).$ If one wishes to modify the ... forcing function to $j\sqrt{2}x(t)$ change the initial condition to $−2y(0)$ and the forcing function to $−2x(t)$
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing functi...
Milicevic3306
16.0k
points
105
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2013-ec
differential-equations
+
–
0
votes
0
answers
23
GATE ECE 2014 Set 1 | Question: 48
For the following feedback system $G(s) = \dfrac{1}{(s+1)(s+2)}.$ The $2\%$-settling time of the step response is required to be less than $2$ seconds. Which one of the following compensators $C(s)$ achieves this? $3\bigg(\dfrac{1}{s+5}\bigg) \\$ $5\bigg(\dfrac{0.03}{s} + 1\bigg) \\$ $2(s+4) \\$ $4\bigg(\dfrac{s+8}{s+3}\bigg)$
For the following feedback system $G(s) = \dfrac{1}{(s+1)(s+2)}.$ The $2\%$-settling time of the step response is required to be less than $2$ seconds.Which one of the fo...
Milicevic3306
16.0k
points
97
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2014-ec-1
differential-equations
+
–
0
votes
0
answers
24
GATE ECE 2014 Set 2 | Question: 5
If the characteristic equation of the differential equation $\frac{\mathrm{d}^2 y}{\mathrm{dx}^2}+2\alpha \frac{\mathrm{d}y}{\mathrm{d} x}+y= 0$ has two equal roots, then the value of $\alpha$ are $\pm 1$ $0,0$ $\pm j$ $\pm 1/2$
If the characteristic equation of the differential equation $$\frac{\mathrm{d}^2 y}{\mathrm{dx}^2}+2\alpha \frac{\mathrm{d}y}{\mathrm{d} x}+y= 0$$ has two equal roots, th...
Milicevic3306
16.0k
points
85
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-2
differential-equations
+
–
0
votes
0
answers
25
GATE ECE 2012 | Question: 34
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)\big|_{t=0^-}=-2$ and $\frac{dy}{dt}\big|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}\big|_{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation$\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)\big|_{t=0^-}=-2$ and $\frac{dy}{dt}\big|_{t=0^-}=0$.The numerical val...
Milicevic3306
16.0k
points
107
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2012-ec
differential-equations
+
–
0
votes
0
answers
26
GATE ECE 2014 Set 4 | Question: 26
With initial values $y(0) =y’(0)=1$, the solution of the differential equation $\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$ at $x=1$ is ________
With initial values $y(0) =y’(0)=1$, the solution of the differential equation $$\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$$ at $x=1$ is ________
Milicevic3306
16.0k
points
79
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-4
numerical-answers
differential-equations
+
–
0
votes
0
answers
27
GATE ECE 2014 Set 4 | Question: 4
If $a$ and $b$ are constants, the most general solution of the differential equation $\frac{d^2x}{dt^2}+2 \frac{dx}{dt}+x=0$ is $ae^{-t}$ $ae^{-t} + bte^{-t}$ $ae^t+bte^{-t}$ $ae^{-2t}$
If $a$ and $b$ are constants, the most general solution of the differential equation $$\frac{d^2x}{dt^2}+2 \frac{dx}{dt}+x=0$$ is$ae^{-t}$$ae^{-t} + bte^{-t}$$ae^t+bte^{-...
Milicevic3306
16.0k
points
74
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-4
differential-equations
+
–
0
votes
0
answers
28
GATE ECE 2012 | Question: 12
With initial condition $x(1)=0.5$, the solution of the differential equation, $t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$ $x=t^2-\frac{1}{2}$ $x=\frac{t^2}{2}$ $x=\frac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation,$$t\frac{dx}{dt}+x=t$$ is$x=t-\frac{1}{2}$$x=t^2-\frac{1}{2}$$x=\frac{t^2}{2}$$x=\frac{t}{2}$...
Milicevic3306
16.0k
points
81
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2012-ec
differential-equations
+
–
0
votes
0
answers
29
GATE ECE 2018 | Question: 34
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{x}.$ The equation that describes the curve is $\ln\left (1+\dfrac{y^{2}}{x^{2}}\right)=x-1$ ... $\ln\left (1+\dfrac{y}{x}\right)=x-1$ $\dfrac{1}{2}\ln\left (1+\dfrac{y}{x}\right)=x-1$
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{...
gatecse
1.6k
points
114
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
0
answers
30
GATE ECE 2018 | Question: 50
The position of a particle $y\left ( t \right )$ is described by the differential equation: $\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$ The initial conditions are $y\left ( 0 \right )=1$ and $\frac{dy}{dt}\mid_{t=0}=0$. The position (accurate to two decimal places) of the particle at $t=\pi$ is _________.
The position of a particle $y\left ( t \right )$ is described by the differential equation:$$\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$$The initial conditions ar...
gatecse
1.6k
points
111
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
numerical-answers
differential-equations
second-order-differential-equation
+
–
0
votes
0
answers
31
GATE ECE 2018 | Question: 4
Let the input be $u$ and the output be $y$ ... $y=au+b,b\neq 0$ $y=au$
Let the input be $u$ and the output be $y$ of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:$\d...
gatecse
1.6k
points
107
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
0
answers
32
GATE ECE 2018 | Question: 12
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and $y = 2$, then the relation between $a$ and $b$ is $a=\dfrac{b}{4}$ $a=\dfrac{b}{2}$ $a=2b$ $a=4b$
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and ...
gatecse
1.6k
points
94
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
partial-differential-equations
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GATE ECE 2017 Set 2 | Question: 2
The general solution of the differential equation $\frac{d^2y}{dx^2}+2\frac{dy}{dx}-5y=0$ in terms of arbitrary constants $K_1$ and $K_2$ is $K_1e^{(-1+\sqrt{6})x}+K_2e^{(-1-\sqrt{6})x}$ $K_1e^{(-1+\sqrt{8})x}+K_2e^{(-1-\sqrt{8})x}$ $K_1e^{(-2+\sqrt{6})x}+K_2e^{(-2-\sqrt{6})x}$ $K_1e^{(-2+\sqrt{8})x}+K_2e^{(-2-\sqrt{8})x}$
The general solution of the differential equation $\frac{d^2y}{dx^2}+2\frac{dy}{dx}-5y=0$in terms of arbitrary constants ...
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Differential Equations
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differential-equations
second-order-differential-equation
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34
GATE ECE 2017 Set 1 | Question: 29
Which one of the following is the general solution of the first order differential equation $\frac{dy}{dx}=(x+y-1)^{2},$ where $x,y$ are real? $y=1+x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1+x+\tan(x+c)$, where $c$ is a constant $y=1-x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1-x+\tan(x+c)$, where $c$ is a constant
Which one of the following is the general solution of the first order differential equation $$\frac{dy}{dx}=(x+y-1)^{2},$$ where $x,y$ are real?$y=1+x+\tan^{-1}(x+c)$, wh...
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Nov 17, 2017
Differential Equations
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differential-equations
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