Recent questions and answers in Partial Differential Equation (PDE) / GO Civil

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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

In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$$$D(\theta)\frac{\partial^2\theta}{\partia...

go_editor

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go_editor asked Feb 27, 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

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...

go_editor

5.3k points

go_editor asked Feb 13, 2020

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3

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 ________.

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\ \si...

go_editor

5.3k points

go_editor asked 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$

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...

gatecse

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gatecse asked Aug 7, 2019

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5

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 $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...

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 exp...

Arjun

13.0k points

Arjun asked 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 ...

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 $\...

Arjun

13.0k points

Arjun asked Feb 14, 2019

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7

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

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 $[- \pi, \pi ]$ is$f(x) ...

Milicevic3306

11.9k points

Milicevic3306 asked Mar 27, 2018

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8

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

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 \df...

Milicevic3306

11.9k points

Milicevic3306 asked Mar 27, 2018

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9

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 $C \: \cos (kt) \lfloor C_1 e^{(\sqrt{k/\alpha})x} +C_2 e^{-(\sqrt{k/\alpha})x} \rfloor \\$ ... $C \sin(kt) \lfloor C_1 \cos \big( \sqrt{k/ \alpha} \big) x + C_2 \sin ( - \sqrt{k/ \alpha} ) x \rfloor$

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 ...

Milicevic3306

11.9k points

Milicevic3306 asked Mar 27, 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 ________

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 ...

Milicevic3306

11.9k points

Milicevic3306 asked 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 $x=1.2$? __________

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} = ...

Milicevic3306

11.9k points

Milicevic3306 asked Mar 25, 2018

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12

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 _______ $1$ $2$ $4$ $6$

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 condit...

praveenkumar_new

140 points

praveenkumar_new answered Feb 18, 2018