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Recent questions and answers in Differential equations
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GATE CH 2021 | Question: 36
For the ordinary differential equation $\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$ with ... $3$ decimal places).
For the ordinary differential equation $$\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$$ with initial conditions $y(0)=y’(0) = y’’(0)=y’’’(0)...
go_editor
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go_editor
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Mar 1, 2021
Differential equations
gatech-2021
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GATE Chemical 2020 | Question: 54
Given $\dfrac{dy}{dx}=y-20$, and $y \mid_{x=0}=40$, the value of $y$ at $x=2$ is _________ (round off to nearest integer)
soujanyareddy13
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soujanyareddy13
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Nov 16, 2020
Differential equations
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GATE Chemical 2020 | Question: 4
Consider the following unit step function.The Laplace transform of this function is$\dfrac{e^{-3s}}{s} \\ $$\dfrac{e^{-3s}}{s^2} \\$$\dfrac{e^{-3s}}{3s} \\$$\dfrac{e^{-6s...
soujanyareddy13
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soujanyareddy13
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Nov 16, 2020
Differential equations
gate2020
differential-equations
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GATE Chemical 2019 | Question: 26
The solution of the ordinary differential equation$\frac{dy}{dx}+3y=1$, subjects to the initial condition $y=1$ at $x=0$, is$\frac{1}{3}\left ( 1+2e^{-x/3} \right )$$\fra...
Arjun
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Arjun
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Feb 24, 2019
Differential equations
gate2019
differential-equations
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GATE Chemical 2017 | Question: 26
For the initial value problem$$\frac{dx}{dt}=\sin\left ( t \right ),\:\:\:\:x\left ( 0 \right )=0$$the value of $x$ at $t=\pi /3$ , is _____________.
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Differential equations
gate2017
numerical-answers
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GATE Chemical 2017 | Question: 27
The Laplace transform of a function is $\frac{s+1}{s\left ( s+2 \right )}$The initial and final values, respectively, of the function are $0$ and $1$$1$ and $\frac{1}{2}$...
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Differential equations
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differential-equations
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GATE Chemical 2016 | Question: 2
The Laplace transform of $e^{at}\sin\left ( bt \right )$ is$\frac{b}{\left ( s-a \right )^{2}+b^{2}}$$\frac{s-a}{\left ( s-a \right )^{2}+b^{2}}$$\frac{s-a}{\left ( s-a \...
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Differential equations
gate2016
differential-equations
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GATE Chemical 2016 | Question: 27
What is the solution for the second order differential equation $\frac{\mathrm{d} ^{2}y}{\mathrm{d} x}^{2}+y=0$, with the initial conditions $y\left | _{x-0}=5\:and\:\fra...
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Differential equations
gate2016
differential-equations
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GATE Chemical 2015 | Question: 13
Consider a linear ordinary differential equation: $\frac{dy}{dx}+p\left ( x \right )y=r\left ( x \right )$. Functions $p\left ( x \right )$ and $r\left ( x \right )$ are...
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Differential equations
gate2015
differential-equations
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GATE Chemical 2014 | Question: 28
The differential equation $\frac{d^{2}y}{dx^{2}}+x^{2}\frac{dy}{dx}+x^{3}y=e^{x}$ is a non-linear differential equation of first degreelinear differential equation of fir...
Milicevic3306
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Milicevic3306
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Mar 25, 2018
Differential equations
gate2014
differential-equations
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GATE Chemical 2014 | Question: 27
The integrating factor for the differential equation$\frac{dy}{dx}-\frac{y}{1+x}=\left ( 1+x \right )$ is$\frac{1}{1+x}$$(1+x)$$x(1+x)$$\frac{x}{1+x}$
Milicevic3306
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Milicevic3306
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Mar 25, 2018
Differential equations
gate2014
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GATE Chemical 2014 | Question: 26
Consider the following differential equation$\frac{dy}{dx}=x+In\:\left ( y \right ); y=2 \: at \: x=0$The solution of this equation at $x=0.4$ using Euler method with a s...
Milicevic3306
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Milicevic3306
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Mar 25, 2018
Differential equations
gate2014
numerical-answers
differential-equations
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GATE Chemical 2014 | Question: 2
For the time domain function $f(t)=t^{2}$, which $ONE$ of the following is the Laplace transform of $\int _{0}^{t}f\left ( t \right )dt$?$\frac{3}{s^{4}}$$\frac{1}{4s^{2}...
Milicevic3306
7.9k
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Milicevic3306
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Mar 25, 2018
Differential equations
gate2014
differential-equations
laplace-transforms
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GATE Chemical 2013 | Question: 28
The solution of the differential equation$\frac{d^2y}{dx^2}$ – $\frac{dy}{dx}$ + 0.25y = 0, given y = 0 at x = 0 and $\frac{dy}{dx}$ = 1 at x = 0 isxe$^{0.5x}$ – xe$...
Milicevic3306
7.9k
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Milicevic3306
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Mar 25, 2018
Differential equations
gate2013
differential-equations
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GATE Chemical 2013 | Question: 27
The solution of the differential equation$\frac{dy}{dx}$ – y$^{2}$ = 0, given y=1 at x=0 is$\frac{1}{1+x}$$\frac{1}{1-x}$$\frac{1}{(1-x)^2}$$\frac{x^3}{3}$+1
Milicevic3306
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Milicevic3306
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Mar 25, 2018
Differential equations
gate2013
differential-equations
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GATE Chemical 2012 | Question: 2
If $a$ and $b$ are arbitrary constants, then the solutions to the ordinary differential equation $\dfrac{d^...
Milicevic3306
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Milicevic3306
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Mar 25, 2018
Differential equations
gate2012
differential-equations
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GATE Chemical 2018 | Question: 1
Consider the following two equation:$\frac{dx}{dt}+x+y=0$$\frac{dy}{dt}-x=0$The above set of equations is represented by$\frac{d^{2}y}{dt^{2}}-\frac{dy}{dt}-y=0$$\frac{d^...
gatecse
1.4k
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gatecse
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Feb 20, 2018
Differential equations
gate2018
differential-equations
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