Register

Recent questions tagged differential-equations

0 votes
0 answers
1
GATE2019: 38
What is the solution of the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x}{y}$, with the initial condition, at $x=0, y=1?$ $x^{2}=y^{2}+1$ $y^{2}=x^{2}+1$ $y^{2}=2x^{2}+1$ $x^{2}-y^{2}=0$
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}...
0 votes
0 answers
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 _________________.
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 ap...
0 votes
0 answers
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).
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).
0 votes
0 answers
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} $
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} \\$$\...
0 votes
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 __________
$\dfrac{d^2y}{dx^2}-y=0$. 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 = ...
0 votes
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 __________
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 __________
0 votes
0 answers
9
GATE2013-41
The solution to $\frac {dy}{dx}+y \cot x=\csc x$ is $y=(c+x)\cot x$ $y=(c+x)\csc x$ $y=(c+x)\csc x\cot x$ $y=(c+x)\frac{\csc x}{\cot x}$
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$$y=(c+x)\frac{\csc x}{\cot x}$
0 votes
0 answers
10
GATE2013-39
The Laplace transform of $f(t) = 2t + 6$ is $\frac{1}{s}+\frac{2}{s^2}$ $\frac{3}{s}-\frac{6}{s^2}$ $\frac{6}{s}+\frac{2}{s^2}$ $-\frac{6}{s}+\frac{2}{s^2}$
The Laplace transform of $f(t) = 2t + 6$ is$\frac{1}{s}+\frac{2}{s^2}$$\frac{3}{s}-\frac{6}{s^2}$$\frac{6}{s}+\frac{2}{s^2}$$-\frac{6}{s}+\frac{2}{s^2}$
To see more, click for the full list of questions or popular tags.