GO Civil
Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Questions
Tags
Subjects
Users
Ask
Blogs
New Blog
Exams
Dark Mode
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Recent questions in Ordinary Differential Equation (ODE)
0
votes
0
answers
1
GATE Civil 2021 Set 2 | Question: 26
If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of $y=x\text{ ln}(kx)$ $y=k\text{ ln}(kx)$ $y=x\text{ ln}(x)$ $y=xk\text{ ln}(k)$
go_editor
asked
in
Ordinary Differential Equation (ODE)
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
ordinary-differential-equation
0
votes
0
answers
2
GATE Civil 2021 Set 1 | Question: 26
The solution of the second-order differential equation $\dfrac{d^{2}y}{dx^{2}}+2\dfrac{dy}{dx}+y=0$ with boundary conditions $y\left ( 0 \right )=1$ and $y\left ( 1 \right )=3$ is $e^{-x}+\left ( 3e-1 \right )xe^{-x}$ ... $e^{-x}-\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$
Arjun
asked
in
Ordinary Differential Equation (ODE)
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
ordinary-differential-equation
second-order-differential-equation
0
votes
0
answers
3
GATE2020-CE-1-26
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the solution is $-5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $-10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$
go_editor
asked
in
Ordinary Differential Equation (ODE)
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
ordinary-differential-equation
0
votes
0
answers
4
GATE2020 CE-2-1
The ordinary differential equation $\dfrac{d^2u}{dx^2}$- 2x^2u +\sin x = 0$ is linear and homogeneous linear and nonhomogeneous nonlinear and homogeneous nonlinear and nonhomogeneous
go_editor
asked
in
Ordinary Differential Equation (ODE)
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
ordinary-differential-equation
0
votes
0
answers
5
GATE2020 CE-2-26
An ordinary differential equation is given below $6\dfrac{d^2y}{dx^2}+\frac{dy}{dx}-y=0$ The general solution of the above equation (with constants $C_1$ and $C_2$), is $y(x) = C_1e^\frac{-x}{3} + C_2e^\frac{x}{2}$ $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{-x}{2}$ $ y(x) = C_1xe^\frac{-x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1e^\frac{-x}{3} + C_2xe^\frac{x}{2}$
go_editor
asked
in
Ordinary Differential Equation (ODE)
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
ordinary-differential-equation
0
votes
0
answers
6
GATE2019 CE-1: 44
Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round off to $1$ decimal place), is _________
Arjun
asked
in
Ordinary Differential Equation (ODE)
Feb 14, 2019
by
Arjun
11.6k
points
gate2019-ce-1
ordinary-differential-equation
numerical-answers
0
votes
0
answers
7
GATE2019 CE-2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2-a^2} \\$ $\dfrac{s}{s^2+a^2}$
Arjun
asked
in
Ordinary Differential Equation (ODE)
Feb 12, 2019
by
Arjun
11.6k
points
gate2019-ce-2
ordinary-differential-equation
laplace-transform
0
votes
0
answers
8
GATE2019 CE-2: 28
An ordinary differential equation is given below; $\left ( \dfrac{dy}{dx} \right ) (x \text{ ln } x)=y$ The solution for the above equation is (Note: $K$ denotes a constant in the options) $y=K x \text{ ln } x$ $y=K x e^x$ $y=K x e^{-x}$ $y=K \text{ ln } x$
Arjun
asked
in
Ordinary Differential Equation (ODE)
Feb 12, 2019
by
Arjun
11.6k
points
gate2019-ce-2
ordinary-differential-equation
0
votes
0
answers
9
GATE2016-1-30
The respective expressions for complementary function and particular integral part of the solution of the differential equation $\dfrac{d^4y}{dx^4}+3 \dfrac{d^2y}{dx^2} = 108x^2$ are $\lfloor c_1+c_2x+c_3 \sin \sqrt{3}x+c_4 \cos \sqrt{3} x \rfloor$ ... $\lfloor c_1+c_2x+c_3 \sin \sqrt{3}x+c_4 \cos \sqrt{3} x \rfloor$ and $\lfloor 5x^4 - 12x^2 +c \rfloor$
Milicevic3306
asked
in
Ordinary Differential Equation (ODE)
Mar 28, 2018
by
Milicevic3306
11.9k
points
gate2016-ce-1
ordinary-differential-equation
0
votes
0
answers
10
GATE2017 CE-1: 27
The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is $Q(t)=e^{-t}-1$ $Q(t)=1+ e^{-t}$ $Q(t)=1 -e^t$ $Q(t)=1- e^{-t}$
Milicevic3306
asked
in
Ordinary Differential Equation (ODE)
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2017-ce-1
ordinary-differential-equation
0
votes
0
answers
11
GATE2017 CE-1: 37
Consider the equation $\dfrac{du}{dt}=3t^2+1$ with $u=0$ at $t=0$. This is numerically solved by using the forward Euler method with a step size, $\Delta t=2$. The absolute error in the solution at the end of the first time step is _______.
Milicevic3306
asked
in
Ordinary Differential Equation (ODE)
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2017-ce-1
numerical-answers
ordinary-differential-equation
euler-equations
0
votes
0
answers
12
GATE2015-2-27
Consider the following second order linear differential equation $\dfrac{d^2y}{dx^2} = -12x^2 +24 x – 20$ The boundary conditions are: at $x=0, \: y=5$ and at $x=2, \: y=21$. The value of $y$ at $x=1$ is _________.
Milicevic3306
asked
in
Ordinary Differential Equation (ODE)
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-2
numerical-answers
ordinary-differential-equation
0
votes
0
answers
13
GATE2015-1-28
Consider the following differential equation: $x(y\:dx +x\:dy) \cos \dfrac{y}{x}=y(x\:dy-y\:dx) \sin \dfrac{y}{x}$ Which of the following is the solution of the above equation ($c$ is an arbitrary constant)? $\dfrac{x}{y} \cos \dfrac{y}{x} = c \\$ $\dfrac{x}{y} \sin \dfrac{y}{x} = c \\$ $xy \cos \dfrac{y}{x} = c \\$ $xy \sin \dfrac{y}{x} = c$
Milicevic3306
asked
in
Ordinary Differential Equation (ODE)
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-1
ordinary-differential-equation
0
votes
0
answers
14
GATE2014-2-4
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is $e^{-k_1t} \\$ $e^{-k_2t} \\$ $e^{k_1t} \\$ $e^{k_2t}$
Milicevic3306
asked
in
Ordinary Differential Equation (ODE)
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2014-ce-2
ordinary-differential-equation
0
votes
0
answers
15
GATE Civil 2012 | Question: 30
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is $y=e^{-2x}$ $y=2e^{-2x}$ $y=10.95 e^{-2x}$ $y=36.95 e^{-2x}$
Milicevic3306
asked
in
Ordinary Differential Equation (ODE)
Mar 25, 2018
by
Milicevic3306
11.9k
points
gate2012-ce
ordinary-differential-equation
0
votes
0
answers
16
GATE2018 CE-2: 27
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is $\dfrac{1}{s+a} \\$ $\dfrac{1}{s-a} \\$ $\dfrac{1}{a-s} \\$ $\infty$
gatecse
asked
in
Ordinary Differential Equation (ODE)
Feb 17, 2018
by
gatecse
4.0k
points
gate2018-ce-2
ordinary-differential-equation
laplace-transform
0
votes
0
answers
17
GATE2018 CE-2: 1
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is $x$ $x^2$ $x^{-1}$ $x^{-2}$
gatecse
asked
in
Ordinary Differential Equation (ODE)
Feb 17, 2018
by
gatecse
4.0k
points
gate2018-ce-2
ordinary-differential-equation
0
votes
1
answer
18
GATE2018 CE-1: 38
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ and $\dfrac{dy}{dx}(0) = -1$ is _____
gatecse
asked
in
Ordinary Differential Equation (ODE)
Feb 17, 2018
by
gatecse
4.0k
points
gate2018-ce-1
ordinary-differential-equation
numerical-answers
To see more, click for the
full list of questions
or
popular tags
.
Welcome to GATE Civil Q&A, where you can ask questions and receive answers from other members of the community.
Top Users
Oct 2022
Recent questions in Ordinary Differential Equation (ODE)