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Recent questions tagged ordinarydifferentialequation
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GATE2020CE126
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 $5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$
asked
Feb 28
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce1
ordinarydifferentialequation
engineeringmathematics
0
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0
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2
GATE2020 CE21
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
asked
Feb 13
in
Engineering Mathematics
by
jothee
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2.7k
points)
gate2020ce2
ordinarydifferentialequation
engineeringmathematics
0
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0
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3
GATE2020 CE226
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}$
asked
Feb 13
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
ordinarydifferentialequation
engineeringmathematics
0
votes
0
answers
4
GATE2019 CE2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2a^2} \\$ $\dfrac{s}{s^2+a^2}$
asked
Feb 12, 2019
in
Engineering Mathematics
by
Arjun
(
2.8k
points)
gate2019ce2
ordinarydifferentialequation
engineeringmathematics
laplacetransform
0
votes
0
answers
5
GATE2019 CE2: 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) $y=K x \text{ ln } x$ $y=K x e^x$ $y=K x e^{x}$ $y=K \text{ ln } x$
asked
Feb 12, 2019
in
Ordinary Differential Equation (ODE)
by
Arjun
(
2.8k
points)
gate2019ce2
differentialequation
engineeringmathematics
ordinarydifferentialequation
0
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0
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6
GATE2017 CE1: 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 _______.
asked
Mar 26, 2018
in
Engineering Mathematics
by
Milicevic3306
(
11.9k
points)
gate2017ce1
numericalanswers
ordinarydifferentialequation
engineeringmathematics
eulerequations
0
votes
0
answers
7
GATE2015128
Consider the following differential equation: $x(y\:dx +x\:dy) \cos \dfrac{y}{x}=y(x\:dyy\:dx) \sin \dfrac{y}{x}$ Which of the following is the solution of the above equation ($c$ is an arbitrary constant)? $\dfrac{x}{y} \cos \dfrac{y}{x} = c \\$ $\dfrac{x}{y} \sin \dfrac{y}{x} = c \\$ $xy \cos \dfrac{y}{x} = c \\$ $xy \sin \dfrac{y}{x} = c$
asked
Mar 26, 2018
in
Ordinary Differential Equation (ODE)
by
Milicevic3306
(
11.9k
points)
gate2015ce1
ordinarydifferentialequation
engineeringmathematics
0
votes
0
answers
8
GATE201330
Laplace equation for water flow in soils is given below. $\dfrac{\partial ^2H}{\partial x^2} + \dfrac{\partial ^2H}{\partial y^2} + \dfrac{\partial ^2H}{\partial z^2} = 0$ Head $H$ does not vary in $y$ and $z$ directions. Boundary conditions are: at $x=0$, $H=5$; and $\dfrac{dH}{dx}=1$. What is the value of $H$ at $x=1.2$? __________
asked
Mar 26, 2018
in
Engineering Mathematics
by
Milicevic3306
(
11.9k
points)
gate2013ce
numericalanswers
ordinarydifferentialequation
engineeringmathematics
laplaceequation
0
votes
0
answers
9
GATE2018 CE2: 27
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(sa) >0$, is $\dfrac{1}{s+a} \\$ $\dfrac{1}{sa} \\$ $\dfrac{1}{as} \\$ $\infty$
asked
Feb 17, 2018
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2018ce2
ordinarydifferentialequation
engineeringmathematics
laplacetransform
0
votes
0
answers
10
GATE2018 CE2: 1
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is $x$ $x^2$ $x^{1}$ $x^{2}$
asked
Feb 17, 2018
in
Ordinary Differential Equation (ODE)
by
gatecse
(
3.9k
points)
gate2018ce2
differentialequation
ordinarydifferentialequation
engineeringmathematics
0
votes
1
answer
11
GATE2018 CE1: 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 _____
asked
Feb 17, 2018
in
Ordinary Differential Equation (ODE)
by
gatecse
(
3.9k
points)
gate2018ce1
differentialequation
numericalanswers
ordinarydifferentialequation
engineeringmathematics
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