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Recent questions in Partial Differential Equation (PDE)

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GATE2020-CE-1-1
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 non-linear equation a second degree non-linear equation

go_editor asked in Partial Differential Equation (PDE) Feb 28, 2020

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GATE2020 CE-2-4
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

go_editor asked in Partial Differential Equation (PDE) Feb 13, 2020

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GATE2020 CE-2-39
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by $ x-x^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 ________.

go_editor asked in Partial Differential Equation (PDE) Feb 13, 2020

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GATE2017 CE-2-29
Consider the following second-order differential equation: $y’’ – 4y’+3y =2t -3t^2$. The particular solution of the differential solution equation is $ – 2 -2t-t^2$ $ – 2t-t^2$ $2t-3t^2$ $ – 2 -2t-3 t^2$

gatecse asked in Partial Differential Equation (PDE) Aug 7, 2019

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GATE2019 CE-1: 2
Consider a two-dimensional 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 $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...

Arjun asked in Partial Differential Equation (PDE) Feb 14, 2019

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GATE2019 CE-1: 27
A one-dimensional domain is discretized into $N$ sub-domains of width $\Delta x$ with node numbers $i=0,1,2,3, \dots , N$. If the time scale is discretized in steps of $\Delta t$, the forward-time and centered-space finite difference approximation at i th node and n th time step, for the ...

Arjun asked in Partial Differential Equation (PDE) Feb 14, 2019

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GATE2016-2-3
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 $[- \pi, \pi ]$ ... $\Sigma_{n-1}^{\infty} \dfrac{(-1)^{n+1}}{2n-1} = \dfrac{\pi}{4}$

Milicevic3306 asked in Partial Differential Equation (PDE) Mar 28, 2018

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GATE2016-1-2
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

Milicevic3306 asked in Partial Differential Equation (PDE) Mar 28, 2018

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GATE2016-1-5
The solution of the partial differential equation $\dfrac{\partial u}{\partial t} = \alpha \dfrac{\partial ^2 u}{\partial x^2}$ is of the form $C \: \cos (kt) \lfloor C_1 e^{(\sqrt{k/\alpha})x} +C_2 e^{-(\sqrt{k/\alpha})x} \rfloor \\$ ... $C \sin(kt) \lfloor C_1 \cos \big( \sqrt{k/ \alpha} \big) x + C_2 \sin ( - \sqrt{k/ \alpha} ) x \rfloor$

Milicevic3306 asked in Partial Differential Equation (PDE) Mar 28, 2018

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GATE2017 CE-1: 20
Consider the following partial differential equation: $3 \frac{\partial ^2 \phi}{ \partial x^2} + B \frac{ \partial ^2 \phi}{\partial x \partial y} + 3 \frac{\partial ^2 \phi}{\partial y^2} + 4 \phi =0$ For this equation to be classified as parabolic, the value of $B^2$ must be ________

Milicevic3306 asked in Partial Differential Equation (PDE) Mar 26, 2018

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GATE Civil 2013 | Question: 30
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 $x=1.2$? __________

Milicevic3306 asked in Partial Differential Equation (PDE) Mar 26, 2018

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GATE2018 CE-1: 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 _______ $1$ $2$ $4$ $6$

gatecse asked in Partial Differential Equation (PDE) Feb 17, 2018

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