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Recent questions tagged partialdifferentialequation
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GATE2020CE11
In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$ ... The above equation is a second order linear equation a second degree linear equation a second order nonlinear equation a second degree nonlinear equation
asked
Feb 28
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce1
partialdifferentialequation
engineeringmathematics
0
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0
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2
GATE2020 CE24
The following partial differential equation is defined for $u:u (x,y)$ $\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x \leq x_2$ The set of auxiliary ... the equation uniquely, is three initial conditions three boundary conditions two initial conditions and one boundary condition one initial condition and two boundary conditions
asked
Feb 13
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
partialdifferentialequation
engineeringmathematics
0
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0
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3
GATE2020 CE239
The Fourier series to represent $x x^2$ for $\pi\leq x\leq \pi$ is given by $ xx^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \sin nx$ The value of $a_0$(round off to two decimal places), is ________.
asked
Feb 13
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
numericalanswers
partialdifferentialequation
engineeringmathematics
0
votes
0
answers
4
GATE2017 CE22
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
asked
Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017ce2
engineeringmathematics
partialdifferentialequation
+1
vote
0
answers
5
GATE2019 CE1: 2
Consider a twodimensional flow through isotropic soil along $x$ direction and $z$ direction. If $h$ is the hydraulic head, the Laplace's equation of continuity is expressed as $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...
asked
Feb 14, 2019
in
Partial Differential Equation (PDE)
by
Arjun
(
2.8k
points)
gate2019ce1
laplaceequation
continuity
partialdifferentialequation
engineeringmathematics
0
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0
answers
6
GATE201623
The Fourier series of the function, $\begin{array}{rll} f(x) & =0, & \pi < x \leq 0 \\ {} & =\pi  x, & 0 < x < \pi \end{array}$ in the interval $[ \pi, \pi ]$ ... $\Sigma_{n1}^{\infty} \dfrac{(1)^{n+1}}{2n1} = \dfrac{\pi}{4}$
asked
Mar 28, 2018
in
Engineering Mathematics
by
Milicevic3306
(
11.9k
points)
gate2016ce2
partialdifferentialequation
engineeringmathematics
fourierseries
0
votes
0
answers
7
GATE201612
The type of partial differential equation $\dfrac{\partial ^2 P}{\partial x^2} + \dfrac{\partial ^2 P}{\partial y^2}+3 \dfrac{\partial ^2 P}{\partial x \partial y}+ 2 \dfrac{\partial P}{\partial x} – \dfrac{\partial P}{\partial y} = 0$ is elliptic parabolic hyperbolic none of these
asked
Mar 28, 2018
in
Engineering Mathematics
by
Milicevic3306
(
11.9k
points)
gate2016ce1
partialdifferentialequation
engineeringmathematics
0
votes
0
answers
8
GATE201615
The solution of the partial differential equation $\dfrac{\partial u}{\partial t} = \alpha \dfrac{\partial ^2 u}{\partial x^2}$ is of the form $C \: \cos (kt) \lfloor C_1 e^{(\sqrt{k/\alpha})x} +C_2 e^{(\sqrt{k/\alpha})x} \rfloor \\$ ... $C \sin(kt) \lfloor C_1 \cos \big( \sqrt{k/ \alpha} \big) x + C_2 \sin (  \sqrt{k/ \alpha} ) x \rfloor$
asked
Mar 28, 2018
in
Engineering Mathematics
by
Milicevic3306
(
11.9k
points)
gate2016ce1
partialdifferentialequation
engineeringmathematics
0
votes
1
answer
9
GATE2018 CE1: 37
The solution at $x=1$, $t=1$ of the partial differential equation $\dfrac{\partial ^2 u}{\partial x^2} = 25 \dfrac{\partial ^2 u}{\partial t^2}$ subject to initial conditions of $u(0) = 3x$ and $\dfrac{\partial u}{\partial t}(0) =3$ is _______ $1$ $2$ $4$ $6$
asked
Feb 17, 2018
in
Partial Differential Equation (PDE)
by
gatecse
(
3.9k
points)
gate2018ce1
partialdifferentialequation
engineeringmathematics
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