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Recent questions tagged differential-equations
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GATE2019: 38
What is the solution of the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x}{y}$, with the initial condition, at $x=0, y=1?$ $x^{2}=y^{2}+1$ $y^{2}=x^{2}+1$ $y^{2}=2x^{2}+1$ $x^{2}-y^{2}=0$
soujanyareddy13
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Nov 3, 2020
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soujanyareddy13
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gate2019
differential-equations
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2
GATE2019: 39
The Laplace transform of the function $f\left ( t \right )=t^{2}+2t+1$ is $\dfrac{1}{s^{3}}+\dfrac{3}{s^{2}}+\dfrac{1}{s} \\$ $\dfrac{4}{s^{3}}+\dfrac{4}{s^{2}}+\dfrac{1}{s} \\$ $\dfrac{1}{s^{3}}+\dfrac{2}{s^{2}}+\dfrac{1}{s} \\$ $\dfrac{2}{s^{3}}+\dfrac{2}{s^{2}}+\dfrac{1}{s}$
soujanyareddy13
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Nov 3, 2020
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soujanyareddy13
2.7k
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gate2019
differential-equations
laplace-transforms
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0
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3
GATE2020: 25
A variable $Y$ is a function of $t$. Given that $Y\left ( t=0 \right )=1$ and $Y\left ( t=1 \right )=2,\dfrac{dY}{dt}$ in the interval $t=\left [ 0,1 \right ]$ can be approximated as _________________.
soujanyareddy13
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Nov 3, 2020
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soujanyareddy13
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gate2020
numerical-answers
differential-equations
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0
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4
GATE2020: 18
Given that $Z=X^{2}+Y^{2}$, the value of $\dfrac{\partial Z}{\partial X}$ for $X=1$ and $Y=0$ is ________________ (answer is an integer).
soujanyareddy13
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gate2020
numerical-answers
differential-equations
partial-differential-equation
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0
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5
GATE2019: 12
Which one of the following equations represents a one-dimensional wave equation? $\dfrac{\partial u}{\partial t}=C^{2}\dfrac{\partial ^{2}u}{\partial x^{2}} \\$ $\dfrac{\partial ^{2}u}{\partial t^{2}}=C^{2}\dfrac{\partial ^{2}u}{\partial x^{2}} \\$ ... $\dfrac{\partial ^{2}u}{\partial t^{2}}+\dfrac{\partial ^{2}u}{\partial x^{2}}=0$
soujanyareddy13
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Nov 3, 2020
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soujanyareddy13
2.7k
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gate2019
differential-equations
partial-differential-equation
0
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0
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6
GATE2016-24
The Laplace transform $F(s)$ of the function $f(t) = \cos (at)$, where $a$ is constant, _________ $\dfrac{s^2}{s^2+a^2} \\$ $\dfrac{a}{s^2+a^2} \\$ $\dfrac{s}{s^2+a^2} \\$ $\dfrac{s}{s^2-a^2} $
Milicevic3306
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Differential Equations
Mar 26, 2018
by
Milicevic3306
7.9k
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gate2016
differential-equations
laplace-transforms
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0
answers
7
GATE2016-53
$\dfrac{d^2y}{dx^2}-y=0$. The conditions for this second order homogeneous differential equation are $y(0)=1$ and $\dfrac{dy}{dx}=3$ at $x=0$. The value of $y$ when $x = 2$ is __________
Milicevic3306
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Differential Equations
Mar 26, 2018
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Milicevic3306
7.9k
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gate2016
numerical-answers
differential-equations
0
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0
answers
8
GATE2017-16
For $y=f(x)$, if $\dfrac{d^2y}{dx^2}=0$, $\dfrac{dy}{dx}=0$ at $x=0$, and $y=1$ at $x=1$, the value of $y$ at $x=2$ is __________
Milicevic3306
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Differential Equations
Mar 26, 2018
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Milicevic3306
7.9k
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gate2017
differential-equations
numerical-answers
0
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0
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9
GATE2013-41
The solution to $\frac {dy}{dx}+y \cot x=\csc x$ is $y=(c+x)\cot x$ $y=(c+x)\csc x$ $y=(c+x)\csc x\cot x$ $y=(c+x)\frac{\csc x}{\cot x}$
Milicevic3306
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Differential Equations
Mar 26, 2018
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Milicevic3306
7.9k
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gate2013
differential-equations
0
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0
answers
10
GATE2013-39
The Laplace transform of $f(t) = 2t + 6$ is $\frac{1}{s}+\frac{2}{s^2}$ $\frac{3}{s}-\frac{6}{s^2}$ $\frac{6}{s}+\frac{2}{s^2}$ $-\frac{6}{s}+\frac{2}{s^2}$
Milicevic3306
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Differential Equations
Mar 26, 2018
by
Milicevic3306
7.9k
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gate2013
differential-equations
laplace-transforms
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