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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
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Feb 28
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jothee
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gate2020ce1
partialdifferentialequation
engineeringmathematics
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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
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Feb 13
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jothee
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gate2020ce2
partialdifferentialequation
engineeringmathematics
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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 ________.
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Feb 13
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jothee
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gate2020ce2
numericalanswers
partialdifferentialequation
engineeringmathematics
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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 $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
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Aug 7, 2019
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gatecse
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gate2017ce2
engineeringmathematics
partialdifferentialequation
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0
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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 $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...
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Feb 14, 2019
in
Partial Differential Equation (PDE):
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Arjun
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2.8k
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gate2019ce1
laplaceequation
continuity
partialdifferentialequation
engineeringmathematics
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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 $[ \pi, \pi ]$ ... $\Sigma_{n1}^{\infty} \dfrac{(1)^{n+1}}{2n1} = \dfrac{\pi}{4}$
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Mar 28, 2018
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Milicevic3306
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gate2016ce2
partialdifferentialequation
engineeringmathematics
fourierseries
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0
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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
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Mar 28, 2018
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Milicevic3306
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gate2016ce1
partialdifferentialequation
engineeringmathematics
0
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0
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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 $C \: \cos (kt) \lfloor C_1 e^{(\sqrt{k/\alpha})x} +C_2 e^{(\sqrt{k/\alpha})x} \rfloor \\$ ... $C \sin(kt) \lfloor C_1 \cos \big( \sqrt{k/ \alpha} \big) x + C_2 \sin (  \sqrt{k/ \alpha} ) x \rfloor$
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Mar 28, 2018
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Milicevic3306
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gate2016ce1
partialdifferentialequation
engineeringmathematics
0
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1
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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 _______ $1$ $2$ $4$ $6$
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Feb 17, 2018
in
Partial Differential Equation (PDE):
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gatecse
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3.9k
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gate2018ce1
partialdifferentialequation
engineeringmathematics
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