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Recent questions and answers in Differential Equations
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GATE2020EC: 3
The partial derivative of the function $f(x, y, z) = e^{1x\cos y} + xze^{1/(1+y^{2})}$ with respect to $x$ at the point $(1,0,e)$ is $1$ $0$ $1 \\$ $\dfrac{1}{e}$
asked
Feb 13
in
Differential Equations
by
jothee
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1.4k
points)
gate2020ec
partialdifferentialequations
engineeringmathematics
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2
GATE2020EC: 27
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y1 \right )x?$ $\ln\mid y1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=2x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=2x^{2}+C$ and $y=1$
asked
Feb 13
in
Differential Equations
by
jothee
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1.4k
points)
gate2020ec
differentialequations
engineeringmathematics
0
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0
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3
GATE2019 EC: 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
asked
Feb 12, 2019
in
Differential Equations
by
Arjun
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1.4k
points)
gate2019ec
differentialequations
engineeringmathematics
0
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0
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4
GATE2019 EC: 19
The value of the integral $\int_{0}^{\pi} \int_{y}^{\pi}\dfrac{\sin x}{x}dx\: dy ,$ is equal to __________.
asked
Feb 12, 2019
in
Differential Equations
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
engineeringmathematics
differentialequations
0
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0
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5
GATE2019 EC: 26
Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(1)=0$ and $ \mid f’(x) \mid \leq 2.$ Given these conditions, which one of the following inequalities is necessarily true for all $x \in[2,2]?$ $f(x)\leq \frac{1}{2} \mid x+1 \mid$ $f(x)\leq 2 \mid x+1 \mid $ $f(x)\leq \frac{1}{2} \mid x \mid$ $f(x)\leq 2 \mid x \mid$
asked
Feb 12, 2019
in
Differential Equations
by
Arjun
(
1.4k
points)
gate2019ec
engineeringmathematics
differentialequations
0
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0
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6
GATE2019 EC: 29
It is desired to find a threetap casual filter which gives zero signal as an output to an input of the form $x[n]= c_{1}exp\left(\dfrac{j\pi n}{2}\right)+c_{2}\left(\dfrac{j\pi n}{2}\right),$ where $c_{1}$ and $c_{2}$ ... $n$, when $x[n]$ is as given above ? $a=1,b=1$ $a=0,b=1$ $a=1,b=1$ $a=0,b=1$
asked
Feb 12, 2019
in
Differential Equations
by
Arjun
(
1.4k
points)
gate2019ec
differentialequations
engineeringmathematics
0
votes
0
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7
GATE2019 EC: 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________.
asked
Feb 12, 2019
in
Differential Equations
by
Arjun
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1.4k
points)
gate2019ec
numericalanswers
differentialequations
engineeringmathematics
0
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0
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8
GATE201613
Given the following statements about a function $f: \Bbb R \rightarrow \Bbb R$, select the right option: P: If $f(x)$ is continuous at $x = x_0$ then it is also differentiable at $x = x_0$. Q: If $f(x)$ is continuous at $x = x_0$ ... , R is false P is false, Q is true, R is true P is false, Q is true, R is false P is true, Q is false, R is true
asked
Mar 28, 2018
in
Differential Equations
by
Milicevic3306
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15.8k
points)
gate2016ec1
differentialequations
engineeringmathematics
0
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0
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9
GATE201532
The contour on the $xy$ plane, where the partial derivative of $x^{2} + y^{2}$ with respect to $y$ is equal to the partial derivative of $6y+4x$ with respect to $x$, is $y=2$ $x=2$ $x+y=4$ $xy=0$
asked
Mar 28, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2015ec3
partialdifferentialequations
engineeringmathematics
0
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0
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10
GATE2015328
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 ________.
asked
Mar 28, 2018
in
Differential Equations
by
Milicevic3306
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15.8k
points)
gate2015ec3
numericalanswers
differentialequations
engineeringmathematics
0
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0
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11
GATE201524
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)}$ $\tan x – \cot y = c\:\text{(c is a constant)}$ $\tan y + \cot x = c\:\text{(c is a constant)}$ $\tan x + \cot y = c\:\text{(c is a constant)}$
asked
Mar 28, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2015ec2
differentialequations
engineeringmathematics
0
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0
answers
12
GATE201444
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 $ae^{t}$ $ae^{t} + bte^{t}$ $ae^t+bte^{t}$ $ae^{2t}$
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2014ec4
differentialequations
engineeringmathematics
0
votes
0
answers
13
GATE2014426
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 ________
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2014ec4
numericalanswers
differentialequations
engineeringmathematics
0
votes
0
answers
14
GATE201432
Which $ONE$ of the following is a linear nonhomogeneous differential equation, where $x$ and $y$ are the independent and dependent variables respectively? $\frac{dy}{dx}+xy= e^{x}$ $\frac{dy}{dx}+xy= 0$ $\frac{dy}{dx}+xy= e^{y}$ $\frac{dy}{dx}+ e^{y}= 0$
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
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15.8k
points)
gate2014ec3
engineeringmathematics
differentialequations
0
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0
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15
GATE201435
If $z= xy \text{ ln} (xy)$, then $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}= 0 \\$ $y\frac{\partial z}{\partial x}= x\frac{\partial z}{\partial y} \\$ $x\frac{\partial z}{\partial x}= y\frac{\partial z}{\partial y} \\$ $y\frac{\partial z}{\partial x}+x\frac{\partial z}{\partial y}= 0$
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2014ec3
partialdifferentialequations
engineeringmathematics
0
votes
0
answers
16
GATE201425
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 $\pm 1$ $0,0$ $\pm j$ $\pm 1/2$
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2014ec2
differentialequations
0
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0
answers
17
GATE2014125
The force on a point charge $+q$ kept at a distance $d$ from the surface of an infinite grounded metal plate in a medium of permittivity $\epsilon\:$ is $0$ $\dfrac{q^{2}}{16\pi \epsilon d^{2}}$ away from the plate $\dfrac{q^{2}}{16\pi \epsilon d^{2}}$ towards the plate $\dfrac{q^{2}}{4\pi \epsilon d^{2}}$ towards the plate
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2014ec1
differentialequations
0
votes
0
answers
18
GATE2014145
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 $0.2 + 0.8e^{5t}$ $0.2  0.2e^{5t}$ $0.8 + 0.2e^{5t}$ $0.8  0.8e^{5t}$
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2014ec1
differentialequations
engineeringmathematics
0
votes
0
answers
19
GATE2014148
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? $3\bigg(\dfrac{1}{s+5}\bigg) \\$ $5\bigg(\dfrac{0.03}{s} + 1\bigg) \\$ $2(s+4) \\$ $4\bigg(\dfrac{s+8}{s+3}\bigg)$
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2014ec1
differentialequations
0
votes
0
answers
20
GATE201337
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 system so that ... the forcing function to $j\sqrt{2}x(t)$ change the initial condition to $−2y(0)$ and the forcing function to $−2x(t)$
asked
Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2013ec
differentialequations
0
votes
0
answers
21
GATE201336
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 $x(t) = \begin{cases} 1&0<t<2 \\ 0&\text{otherwise} \end{cases}$ Assuming that $y(0) = 0$ and ... $\frac{e^{2s}}{(s+2)(s+3)} \\$ $\frac{1e^{2s}}{s(s+2)(s+3)} $
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Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
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gate2013ec
differentialequations
0
votes
0
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22
GATE201322
The transfer function $\dfrac{V_{2}(s)}{V_{1}(s)}$ of the circuit shown below is $\frac{0.5s+1}{s+1} \\ $ $\frac{3s+6}{s+2} \\ $ $\frac{s+2}{s+1} \\ $ $\frac{s+1}{s+2}$
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Mar 26, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
points)
gate2013ec
differentialequations
engineeringmathematics
0
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0
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23
GATE201234
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 $2$ $1$ $0$ $1$
asked
Mar 25, 2018
in
Differential Equations
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Milicevic3306
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15.8k
points)
gate2012ec
engineeringmathematics
differentialequations
0
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0
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24
GATE201222
In the circuit shown below, the current through the inductor is $\frac{2}{1+j}\:A$ $\frac{1}{1+j}\:A$ $\frac{1}{1+j}\:A$ $0\:A$
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Mar 25, 2018
in
Differential Equations
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Milicevic3306
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15.8k
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gate2012ec
differentialequations
engineeringmathematics
0
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25
GATE201212
With initial condition $x(1)=0.5$, the solution of the differential equation, $t\frac{dx}{dt}+x=t$ is $x=t\frac{1}{2}$ $x=t^2\frac{1}{2}$ $x=\frac{t^2}{2}$ $x=\frac{t}{2}$
asked
Mar 25, 2018
in
Differential Equations
by
Milicevic3306
(
15.8k
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gate2012ec
differentialequations
engineeringmathematics
0
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0
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26
GATE201850
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 _________.
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Feb 19, 2018
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Differential Equations
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gatecse
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gate2018ec
numericalanswers
differentialequations
engineeringmathematics
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27
GATE201852
Let $r=x^{2}+yz$ and $z^{3}xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,1,1 \right ),$ the value (correct to two decimal places) of $\dfrac{\partial r}{\partial x}$ is _________ .
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Feb 19, 2018
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Differential Equations
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gatecse
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gate2018ec
numericalanswers
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0
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28
GATE201839
The input $4\sin c(2t)$ is fed to a Hilbert transformer to obtain $y( t),$ as shown in the figure below: Here $\sin c \left ( x\right )=\dfrac{\sin\left ( \pi x \right )}{\pi x}.$ The value (accurate to two decimal places) of $\int ^{\infty }_{\infty } \mid y( t ) \mid ^{2}dt$ is ________.
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Feb 19, 2018
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Differential Equations
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gatecse
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gate2018ec
numericalanswers
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hilberttransformer
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29
GATE201834
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 $\ln\left (1+\dfrac{y^{2}}{x^{2}}\right)=x1$ ... $\ln\left (1+\dfrac{y}{x}\right)=x1$ $\dfrac{1}{2}\ln\left (1+\dfrac{y}{x}\right)=x1$
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Feb 19, 2018
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Differential Equations
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gatecse
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gate2018ec
differentialequations
engineeringmathematics
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30
GATE201812
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 $a=\dfrac{b}{4}$ $a=\dfrac{b}{2}$ $a=2b$ $a=4b$
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Feb 19, 2018
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Differential Equations
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gatecse
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gate2018ec
differentialequations
engineeringmathematics
0
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31
GATE20184
Let the input be $u$ and the output be $y$ ... $y=au+b,b\neq 0$ $y=au$
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Feb 19, 2018
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Differential Equations
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gatecse
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gate2018ec
engineeringmathematics
differentialequations
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32
GATE2017 EC2: 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 $K_1e^{(1+\sqrt{6})x}+K_2e^{(1\sqrt{6})x}$ $K_1e^{(1+\sqrt{8})x}+K_2e^{(1\sqrt{8})x}$ $K_1e^{(2+\sqrt{6})x}+K_2e^{(2\sqrt{6})x}$ $K_1e^{(2+\sqrt{8})x}+K_2e^{(2\sqrt{8})x}$
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Nov 23, 2017
in
Differential Equations
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admin
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2.8k
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gate2017ec2
secondorderdifferentialequation
engineeringmathematics
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33
GATE2017 EC1: 29
Which one of the following is the general solution of the first order differential equation $\frac{dy}{dx}=(x+y1)^{2},$ 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 $y=1x+\tan^{1}(x+c)$, where $c$ is a constant $y=1x+\tan(x+c)$, where $c$ is a constant
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Nov 17, 2017
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Differential Equations
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gate2017ec1
firstorderdifferentialequation
engineeringmathematics
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34
GATE2017 EC1: 30
Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of NewtonRaphson’s method(up to two decimal places) is__________.
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Nov 17, 2017
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gate2017ec1
numericalanswers
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engineeringmathematics
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