Recent questions tagged differential-equations / GO Electrical

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GATE Electrical 2020 | Question: 16
Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is ______________. $\frac{\mathrm{d} y}{\mathrm{d} x}=2x-y,\:\:y\left ( 0 \right )=1$

Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is ______________.$$\frac{\mathrm{d} y}{\mathrm{d} x}=2x-y,\:\...

go_editor

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go_editor asked Feb 28, 2020

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GATE Electrical 2019 | Question: 3
The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}}- C^{2} \bigg( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}} \bigg )=0;$ where $c \neq 0$ is known as heat equation wave equation Poisson’s equation Laplace equation

The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}}- C^{2} \bigg( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}} \bigg )=0;...

Arjun

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Arjun asked Feb 12, 2019

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GATE Electrical 2012 | Question: 38
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla \cdot \textbf{A} = 0$ is $-2$ $2$ $1$ $0$

The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of ...

Andrijana3306

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Andrijana3306 asked Mar 23, 2018

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GATE Electrical 2012 | Question: 14
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is $x=t-\dfrac{1}{2} \\ $ $x=t^2-\dfrac{1}{2} \\ $ $x=\dfrac{t^2}{2} \\$ $x=\dfrac{t}{2}$

With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is$x=t-\dfrac{1}{2} \\ $$x=t^2-\dfrac{1}{2} \\ $$x=\dfrac{t^2}{2} \\$$x...

Andrijana3306

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Andrijana3306 asked Mar 23, 2018

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GATE Electrical 2018 | Question: 33
Consider a system governed by the following equations $ \frac{dx_1(t)}{dt} = x_2(t)-x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)-x_2(t)$ The initial conditions are such that $x_1(0)<x_2(0)< \infty$. Let $x_{1f}= \underset{t \to \infty}{\lim} x_1(t)$ ... $x_{1f}<x_{2f}<\infty$ $x_{2f}<x_{1f}<\infty$ $x_{1f}<=_{2f}<\infty$ $x_{1f}=x_{2f}=\infty$

Consider a system governed by the following equations $$ \frac{dx_1(t)}{dt} = x_2(t)-x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)-x_2(t)$$ The initial conditions are such that $...

Arjun

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Arjun asked Feb 19, 2018

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GATE Electrical 2017 Set 1 | Question: 30
Let a causal LTI system be characterised by the following differential equation, with initial rest condition $\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(t)}{dt}$ where, $x(t)$ and $y(t)$ are the input and output respectively. The impulse response of the system ... $7e^{-2t}u(t)-2e^{-5t}u(t)$ $-7e^{-2t}u(t)+2e^{-5t}u(t)$

Let a causal LTI system be characterised by the following differential equation, with initial rest condition$\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(...

Arjun

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Arjun asked Feb 26, 2017

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GATE Electrical 2017 Set 1 | Question: 27
Consider the differential equation $(t^{2}-81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belongs to the interval $(-2, 2)$ $(-10, 10)$ $(-10, 2)$ $(0, 10)$

Consider the differential equation $(t^{2}-81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belong...

Arjun

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Arjun asked Feb 26, 2017

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GATE Electrical 2014 Set 1 | Question: 3
The solution for the differential equation $\dfrac{d^2x}{dt^2}=-9x,$ with initial conditions $x(0)=1$ and $\dfrac{dx}{dt}\bigg \vert_{t=0}=1$ , is $t^2+t+1 \\$ $\sin 3t+\dfrac{1}{3}\cos3t+\dfrac{2}{3} \\$ $\dfrac{1}{3}\sin3t+\cos 3t \\$ $\cos 3t+t$

The solution for the differential equation $\dfrac{d^2x}{dt^2}=-9x,$ with initial conditions $x(0)=1$ and $\dfrac{dx}{dt}\bigg \vert_{t=0}=1$ , is$t^2+t+1 \\$$\sin 3t+\df...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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9

GATE Electrical 2015 Set 2 | Question: 28
A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

A differential equation $\dfrac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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GATE Electrical 2015 Set 1 | Question: 27
A solution of the ordinary differential equation $\dfrac{d^{2}y}{dt^{2}}+5\dfrac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\dfrac{1-3e}{e^{3}}$. The value of $\dfrac{dy}{dt}(0)$ is _______.

A solution of the ordinary differential equation $\dfrac{d^{2}y}{dt^{2}}+5\dfrac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\dfrac{1-3e}{e^{3}}$. The value of $\df...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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11

GATE Electrical 2016 Set 2 | Question: 30
Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then the value of $y(1)$ is _________.

Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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12

GATE Electrical 2016 Set 2 | Question: 8
The solution of the differential equation, for $t > 0, y"(t)+2y'(t)+y(t)=0$ with initial conditions $y(0)=0$ and $y'(0)=1$, is ($u(t)$ denotes the unit step function), $te^{-t}u(t)$ $(e^{-t}-te^{-t})u(t)$ $(-e^{-t}+te^{-t})u(t)$ $e^{-t}u(t)$

The solution of the differential equation, for $t 0, y"(t)+2y'(t)+y(t)=0$ with initial conditions $y(0)=0$ and $y'(0)=1$, is ($u(t)$ denotes the unit step function),$te^...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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13

GATE Electrical 2016 Set 2 | Question: 4
Consider a causal $LTI$ system characterized by differential equation $\frac{dy(t)}{dt}+\frac{1}{6}y(t)=3x(t)$ The response of the system to the input $x(t)=3e^{-\frac{t}{3}}u(t)$, where $u(t)$ denotes the unit step function, is $9e^{-\frac{t}{3}}u(t)$ ... $54e^{-\frac{t}{6}}u(t)-54e^{-\frac{t}{3}}u(t)$

Consider a causal $LTI$ system characterized by differential equation $\frac{dy(t)}{dt}+\frac{1}{6}y(t)=3x(t)$ The response of the system to the input $x(t)=3e^{-\frac{t}...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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14

GATE Electrical 2016 Set 1 | Question: 4
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation $\dfrac{d^{2}y}{dt^{2}}+2\dfrac{dy}{dt}+y=0$. Then $y(2)$ is $5e^{-1}$ $5e^{-2}$ $7e^{-1}$ $7e^{-2}$

A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation$\dfrac{d^{2}y}{dt^{2}}+2\dfrac{dy}{dt}+y=0$. Then $y(2)$ is$5e^{-1}$$...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017