GATE Mechanical 2021 Set 2 | Question: 2

go_editor asked in Differential Equations Mar 1, 2021 recategorized Apr 11, 2021 by Lakshman Patel RJIT

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If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is

$0$
$\frac{1}{2}$
$1$
$\frac{3}{2}$

gateme-2021-set2
differential-equations
laplace-transforms

go_editor asked in Differential Equations Mar 1, 2021 recategorized Apr 11, 2021 by Lakshman Patel RJIT

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Apply Intitial Value theorem

Hashtag answered Jun 20, 2021

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gatecse asked in Differential Equations Feb 22, 2021

GATE Mechanical 2021 Set 1 | Question: 3
The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$ ... $0$ $\infty$ $e^{sa}$ $e^{-sa}$

gatecse asked in Differential Equations Feb 22, 2021

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go_editor asked in Differential Equations Mar 1, 2021

GATE Mechanical 2021 Set 2 | Question: 28
Consider the following differential equation $\left ( 1+y \right )\frac{dy}{dx}=y.$ The solution of the equation that satisfies condition $y(1)=1$ is $2ye^{y}=e^{x}+e$ $y^{2}e^{y}=e^{x}$ $ye^{y}=e^{x}$ $\left ( 1+y \right )e^{y}=2e^{x}$

go_editor asked in Differential Equations Mar 1, 2021

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go_editor asked in Differential Equations Sep 18, 2020

GATE2020-ME-2: 4
The solution of $\dfrac{d^2y}{dt^2}-y=1,$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is $\dfrac{1}{s(s+1)(s-1)} \\$ $\dfrac{1}{s(s+1)} \\$ $\dfrac{1}{s(s-1)} \\$ $\dfrac{1}{s-1} \\$

go_editor asked in Differential Equations Sep 18, 2020

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Arjun asked in Differential Equations Feb 27, 2017

GATE2017 ME-2: 5
The Laplace transform of $te^{t}$ is $\dfrac{s}{(s+1)^{2}} \\$ $\dfrac{1}{(s-1)^{2}} \\$ $\dfrac{1}{(s+1)^{2}} \\$ $\dfrac{s}{(s-1)}$

Arjun asked in Differential Equations Feb 27, 2017

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gatecse asked in Differential Equations Feb 22, 2021

GATE Mechanical 2021 Set 1 | Question: 1
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$ subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is $0$ $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$

gatecse asked in Differential Equations Feb 22, 2021

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