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Recent questions and answers in Differential equations
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GATE IN 2021 | Question: 6
Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ________________. $\frac{1}{s-1}$ with real part of $s< 1$ $\frac{1}{s-1}$ with real part of $s> 1$ $\frac{-1}{s-1}$ with real part of $s< 1$ $\frac{-1}{s-1}$ with real part of $s> 1$
Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ______________...
Arjun
2.9k
points
Arjun
asked
Feb 19, 2021
Differential equations
gatein-2021
differential-equations
laplace-transform
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2
GATE2020 IN: 27
Consider the differential equation $\frac{dx}{dt}=\sin(x),$ with the initial condition $x(0)=0. $ The solution to this ordinary differential equation is __________ $x(t)=0$ $x(t)=\sin(t)$ $x(t)=\cos(t)$ $x(t)=\sin(t)-\cos(t)$
Consider the differential equation $\frac{dx}{dt}=\sin(x),$ with the initial condition $x(0)=0. $The solution to this ordinary differential equation is __________$x(t)=0$...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Differential equations
gate2020-in
differential-equations
ordinary-differential-equation
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0
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0
answers
3
GATE2020: 2
Consider the recursive equation $X_{n+1}=X_n – h(F(X_n)-X_n),$ with initial condition $X_0=1$ and h>0 being a very small valued scalar. This recursion numerically solves the ordinary differential equation ________ $\dot{X}=-F(X), X(0)=1$ $\dot{X}=-F(X)+X, X(0)=1$ $\dot{X}=F(X), X(0)=1$ $\dot{X}=F(X)+X, X(0)=1$
Consider the recursive equation $X_{n+1}=X_n – h(F(X_n)-X_n),$ with initial condition $X_0=1$ and h>0 being a very small valued scalar. This recursion numerically solve...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Differential equations
gate2020-in
differential-equations
recursive-equation
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–
0
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0
answers
4
GATE2020: 19
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 3, 2020
Differential equations
gate2020-in
numerical-answers
differential-equations
fourier-transform
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–
0
votes
0
answers
5
GATE2017: 35
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 2, 2020
Differential equations
gate2017-in
numerical-answers
differential-equations
laplace-transform
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–
0
votes
0
answers
6
GATE2017: 10
A system is described by the following differential equation: $\frac {dy(t)}{dt}+2y(t)=\frac {dx(t)}{dt}+x(t),\;x(0)=y(0)=0$ where $\text{x(t)}$ and $\text{y(t)}$ are the input and output variables respectively. The transfer function of the inverse system is $\frac {s+1}{s-2}$ $\frac {s+2}{s+1}$ $\frac{s+1}{s+2}$ $\frac {s-1}{s-2}$
A system is described by the following differential equation:$\frac {dy(t)}{dt}+2y(t)=\frac {dx(t)}{dt}+x(t),\;x(0)=y(0)=0$where $\text{x(t)}$ and $\text{y(t)}$ are the i...
soujanyareddy13
2.7k
points
soujanyareddy13
asked
Nov 1, 2020
Differential equations
gate2017-in
differential-equations
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–
0
votes
0
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7
GATE2019 IN: 28
The dynamics of the state $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ of a sytem is governed by the differential equation $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ = $\begin{bmatrix}1 & 2 \\-3 & -4\end{bmatrix}$\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ + $ ... is $\begin{bmatrix}-30 \\-40\end{bmatrix}$ $\begin{bmatrix}-20 \\-10\end{bmatrix}$ $\begin{bmatrix}5\\-15\end{bmatrix}$ $\begin{bmatrix}50 \\-35\end{bmatrix}$
The dynamics of the state $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ of a sytem is governed by the differential equation $\begin{bmatrix}x{_1} \\x{_2}\end{bmatrix}$ = ...
Arjun
2.9k
points
Arjun
asked
Feb 10, 2019
Differential equations
gate2019-in
differential-equations
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–
0
votes
0
answers
8
GATE2014-3
The figure shows the plot of $y$ as a function of $x$ The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is : $\frac{d^2y}{dx^2}=1$ $\frac{dy}{dx}=x$ $\frac{dy}{dx}=-x$ $\frac{dy}{dx}=|x|$
The figure shows the plot of $y$ as a function of $x$The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is :$\fr...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014-in
differential-equations
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–
0
votes
0
answers
9
GATE2014-44
$X(k)$ is the Discrete Fourier Transform of a 6-point real sequence $x(n).$ If $X(0)=9+j0, X(2)=2+j2, X(3)=3-j0, X(5)=1-j1, x(0)$ is $3$ $9$ $15$ $18$
$X(k)$ is the Discrete Fourier Transform of a 6-point real sequence $x(n).$If $X(0)=9+j0, X(2)=2+j2, X(3)=3-j0, X(5)=1-j1, x(0)$ is$3$$9$$15$$18$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014-in
differential-equations
fourier-transform
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–
0
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0
answers
10
GATE2013-38
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$ $\frac{1}{s^2}[1-2e^{-s}+e^{-2s}]$
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013-in
differential-equations
laplace-transform
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–
0
votes
0
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11
GATE2013-37
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$ $2$ $\pi$ $\sqrt{2}$
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013-in
differential-equations
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–
0
votes
0
answers
12
GATE2013-13
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ is Parabolic Elliptic Hyperbolic Nonlinear
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ isParabolicEllipticHyperbolicNonlinear
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013-in
differential-equations
partial-differential-equations
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–
0
votes
0
answers
13
GATE2012-36
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$$1/2$$1$$2$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
fourier-transform
+
–
0
votes
0
answers
14
GATE2012-30
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}|_{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation$\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$.The numerical value of $\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
+
–
0
votes
0
answers
15
GATE2012-2
With initial condition $x(1)=0.5$, the solution of the differential equation, $t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$ $x=t^2-\frac{1}{2}$ $x=\frac{t^2}{2}$ $x=\frac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation,$t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$$x=t^2-\frac{1}{2}$$x=\frac{t^2}{2}$$x=\frac{t}{2}$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
+
–
0
votes
0
answers
16
GATE2012-4
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}.$ The unilateral Laplace transform of $tf(t)$ is $-\frac{s}{(s^2+s+1)^2}$ $-\frac{2s+1}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}.$ The unilateral Laplace transform of $tf(t)$ is$-\frac{s}{(s^2+s+1)^2}$$-\frac{2s+1}{(s^2+s+1)^2}$$\frac...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
laplace-transform
+
–
0
votes
0
answers
17
GATE2018IN: 29
Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy $\frac {\partial {V(x,y)}}{\partial y}$ = x$^2$ + qy$^2$ + 2xy where p and q are constant ,V(x,y) that satisfies the above equations is p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 2xy + 6 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 5 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$ + xy p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$
Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy ...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Differential equations
gate2018-in
differential-equations
partial-differential-equations
+
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