GATE2015-2-28

Arjun asked in Differential Equations Feb 24, 2017 recategorized Mar 4, 2021 by Lakshman Patel RJIT

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Consider the following differential equation:

$\dfrac{dy}{dt}=-5y$; initial condition: $y=2$ at $t=0$.

The value of $y$ at $t=3$ is

$-5e^{-10}$
$2e^{-10}$
$2e^{-15}$
$-15e^{2}$

gateme-2015-set2
differential-equations

Arjun asked in Differential Equations Feb 24, 2017 recategorized Mar 4, 2021 by Lakshman Patel RJIT

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Arjun asked in Differential Equations Feb 24, 2017

GATE2015-2-4
The Laplace transform of $e^{i5t}$ where $i=\sqrt{-1}$, is $\dfrac{s-5i}{s^2-25} \\$ $\dfrac{s+5i}{s^2+25} \\$ $\dfrac{s+5i}{s^2-25} \\$ $\dfrac{s-5i}{s^2+25} $

Arjun asked in Differential Equations Feb 24, 2017

by Arjun

27.4k points

gateme-2015-set2
laplace-transforms
differential-equations

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Arjun asked in Differential Equations Feb 24, 2017

GATE2015-1-28
Find the solution of $\dfrac{d^2y}{dx^2}=Y$ which passes through the origin and the point $\left(\ln 2,\dfrac{3}{4}\right)$ $y=\dfrac{1}{2}e^x-e^{-x} $ $y=\dfrac{1}{2}(e^x+e^{-x}) $ $y=\dfrac{1}{2}(e^x-e^{-x}) $ $y=\dfrac{1}{2}e^x+e^{-x} $

Arjun asked in Differential Equations Feb 24, 2017

by Arjun

27.4k points

gateme-2015-set1
differential-equations

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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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5.0k points

gateme-2021-set2
differential-equations

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Arjun asked in Differential Equations Feb 24, 2017

GATE2015-3-44
Laplace transform of the function $f(t)$ is given by $F(s)=L\begin{bmatrix} f(t) \end{bmatrix}=\int_{0}^{\infty }f(t)e^{-st}dt$ . Laplace transform of the function shown below is given by $\displaystyle{\frac{1-e^{-2s}}{s}} \\$ $\displaystyle{\frac{1-e^{-s}}{2s}} \\$ $\displaystyle{\frac{2-2e^{-s}}{s}} \\$ $\displaystyle{\frac{1-2e^{-s}}{s}}$

Arjun asked in Differential Equations Feb 24, 2017

by Arjun

27.4k points

gateme-2015-set3
differential-equations
laplace-transforms

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Arjun asked in Differential Equations Feb 24, 2017

GATE2015-1-7
The Blasius equation related to boundary layer theory is a third-order linear partial differential equation third-order nonlinear partial differential equation second-order nonlinear ordinary differential equation third-order nonlinear ordinary differential equation

Arjun asked in Differential Equations Feb 24, 2017

by Arjun

27.4k points

gateme-2015-set1
differential-equations
boundary-value-problems

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GATE2015-2-28

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