Recent questions tagged first-order-differential-equation / GO Electronics

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GATE ECE 2024 | Question: 10
A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_{0}}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t=t_{k}$, the variance of the random variable $n\left(t_{k}\right)$ is $\_\_\_\_\_\_\_$. $\frac{N_{0}}{4 R C}$ $\frac{N_{0}}{2 R C}$ $\frac{N_{0}}{R C}$ $\frac{2 N_{0}}{R C}$

A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_{0}}{2}$, when applied to a first-order RC low pass filter produces an output...

admin

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admin asked Feb 16

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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

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admin asked Nov 30, 2022

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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

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admin asked Sep 15, 2022

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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

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admin asked Sep 3, 2022

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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

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Arjun asked Feb 19, 2021

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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...

admin

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admin asked Nov 17, 2017