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Recent questions tagged differentialequation
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GATE2020ME23
Which of the following statements is true about the two sided Laplace transform? It exists for every signal that may or may not have a Fourier transform It has no poles for any bounded signal that is nonzero only inside a finite time interval The ... If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles
asked
Mar 1
in
Others
by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2020ME24
Consider a signal $x[n]=\left(\frac{1}{2}\right)^{n} 1[n]$, where $1[n]= 0$ if $n< 0$, and $1[n]= 1$ if $n\geq0$. The ztransform of $x[nk],k> 0$ is $\dfrac{z^{k}}{1\frac{1}{2}z^{1}}$ with region of convergence being $\mid z \mid < 2$ $\mid z \mid > 2$ $\mid z \mid < \frac{1}{2}$ $\mid z \mid > \frac{1}{2}$
asked
Mar 1
in
Others
by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
differentialequation
0
votes
0
answers
GATE2020ME210
Consider a linear timeinvariant system whose input $r(t)$ and output $y(t)$ are related by the following differential equation: $\frac{d^{2}y(t)}{dt^{2}}+4y(t)=6r(t)$ The poles of this system are at $+2j, 2j$ $+2,2$ $+4,4$ $+4j,4j$
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Mar 1
in
Others
by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
differentialequation
0
votes
0
answers
GATE2020ME1: 3
The Laplace transform of a function $f(t)$ is $L( f )=\frac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is $f\left ( t \right )=\frac{1}{\omega ^{2}}\left ( 1\cos\:\omega t \right )$ $f\left ( t \right )=\frac{1}{\omega}\cos\:\omega t$ $f\left ( t \right )=\frac{1}{\omega}\sin\:\omega t$ $f\left ( t \right )=\frac{1}{\omega^{2}}\left ( 1\sin\:\omega t \right )$
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2020ME1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
numericalanswers
engineeringmathematics
differentialequation
randomvariables
0
votes
0
answers
GATE2019 ME2: 27
A diffferential equation is given as $x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$ The solution of the differential equation in terms of arbitrary constants $C_1$ and $C_2$ is $y=C_1x^2 +C_2 x+2$ $y=\frac{C_1}{x^2} +C_2x+2$ $y=C_1x^2+C_2x+4$ $y=\frac{C_1}{x^2}+C_2x+4$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me2
engineeringmathematics
differentialequation
0
votes
0
answers
GATE2019 ME1: 27
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^22y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is $4xy2x^2+2y^2+ \text{constant}$ $4y^24xy + \text{constant}$ $2x^22y^2+ xy + \text{constant}$ $4xy+2y^22x^2+ \text{constant}$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE201246
Consider the differential equation $x^2 \frac{d^2y}{dx^2}+x\frac{dy}{dx}4y=0$ with the boundary conditions of $y(0)=0$ and $y(1)=1$. The complete solution of the differential equation is $x^2 \\$ $\sin (\frac{\pi x}{2}) \\$ $e^x \sin(\frac{\pi x}{2}) \\$ $e^{x} \sin(\frac{\pi x}{2}) \\$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
differentialequation
boundaryvalueproblems
0
votes
0
answers
GATE2018137
An explicit forward Euler method is used to numerically integrate the differential equation $\frac{dy}{dt} = y$ using a time step of $0.1$. With the initial condition $y(0)=1$, the value of $y(1)$ computed by this method is ________ (correct to two decimal places)
asked
Feb 17, 2018
in
Others
by
Arjun
(
21.2k
points)
gate2018me1
numericalanswers
engineeringmathematics
differentialequation
eulercauchyequations
0
votes
0
answers
GATE2018138
$F(s)$ is the Laplace transform of the function $f(t) =2t^2 e^{t}$. $F(1)$ is _______ (correct to two decimal places).
asked
Feb 17, 2018
in
Others
by
Arjun
(
21.2k
points)
gate2018me1
numericalanswers
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2017 ME1: 4
The differential equation $\frac{d^{2}y}{dx^{2}}+16y=0$ for $y(x)$ with the two boundary conditions $\frac{dy}{dx}\mid _{x=0}=1$ and $\frac{dy}{dx}\mid _{x=\frac{\pi}{2}}=1$ has. No solution. Exactly two solutions. Exactly one solution. Infinitely many solutions.
asked
Feb 27, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2017me1
engineeringmathematics
differentialequation
initialandboundaryvalueproblems
0
votes
0
answers
GATE201633
Solutions of Laplace’s equation having continuous secondorder partial derivatives are called biharmonic functions harmonic functions conjugate harmonic functions error functions
asked
Feb 24, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2016me3
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE201623
Laplace transform of cos( $\omega$t) is $\frac{s}{s^2+\omega ^2}$ $\frac{\omega }{s^2+\omega ^2}$ $\frac{s}{s^2\omega ^2}$ $\frac{\omega }{s^2\omega ^2}$
asked
Feb 24, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2016me2
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2016127
If $y=f(x)$ satisfies the boundary value problem ${y}''+9y=0$ , $y(0)=0$ , $y(\pi /2)=\sqrt{2}$, then $y(\pi /4)$ is ________
asked
Feb 24, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2016me1
numericalanswers
engineeringmathematics
differentialequation
boundaryvalueproblems
0
votes
0
answers
GATE201612
If $f(t)$ is a function defined for all $t$ ≥ $0$, its Laplace transform $F(s)$ is defined as $\int_{0}^{\infty }e^{st}f(t)dt$ $\int_{0}^{\infty }e^{st}f(t)dt$ $\int_{0}^{\infty }e^{ist}f(t)dt$ $\int_{0}^{\infty }e^{ist}f(t)dt$
asked
Feb 24, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2016me1
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2015341
The value of $\int_{C}^{ }[(3x8y^2)dx+(4y6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
asked
Feb 24, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2015me3
numericalanswers
engineeringmathematics
differentialequation
initialandboundaryvalueproblems
0
votes
0
answers
GATE2014429
Consider an ordinary differential equation $\frac{dx}{dt}=4t+4$. If $x = x_0$ at $t = 0$, the increment in $x$ calculated using RungeKutta fourth order multistep method with a step size of $Δt = 0.2$ is $0.22$ $0.44$ $0.66$ $0.88$
asked
Feb 19, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2014me4
engineeringmathematics
differentialequation
0
votes
0
answers
GATE201445
Laplace transform of $\cos(\omega t)$ is $\frac{s}{s^2+\omega ^2}$. The Laplace transform of $e^{2t} \cos(4t)$ is $\frac{s2}{(s2)^2+16} \\$ $\frac{s+2}{(s2)^2+16} \\$ $\frac{s2}{(s+2)^2+16} \\$ $\frac{s+2}{(s+2)^2+16}$
asked
Feb 19, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2014me4
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2014227
The general solution of the differential equation $\frac{dy}{dx}=cos(x+y)$, with $c$ as a constant, is $y+sin(x+y)=x+c$ $tan(\frac{x+y}{2})=y+c$ $cos(\frac{x+y}{2})=x+c$ $tan(\frac{x+y}{2})=x+c$
asked
Feb 19, 2017
in
Others
by
Arjun
(
21.2k
points)
gate2014me2
engineeringmathematics
differentialequation
0
votes
0
answers
GATE201327
The function $f(t)$ satisfies the differential equation $\frac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\frac{d(f)}{d(t)}(0)=4$. The Laplace transform of $f(t)$is given by $\frac{2}{s+1}$ $\frac{4}{s+1}$ $\frac{4}{s^2+1}$ $\frac{2}{s^4+1}$
asked
Feb 19, 2017
in
Others
by
piyag476
(
1.4k
points)
gate2013me
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE20131
The partial differential equation $\frac{\partial u }{\partial t}+u\frac{\partial u}{\partial x}=\frac{\partial^2 u}{\partial x^2}$ is a linear equation of order $2$ nonlinear equation of order $1$ linear equation of order $1$ nonlinear equation of order $2$
asked
Feb 19, 2017
in
Differential Equations
by
piyag476
(
1.4k
points)
gate2013me
engineeringmathematics
differentialequation
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