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Recent activity in Partial Differential Equation (PDE)
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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)$$$\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 12, 2021
Partial Differential Equation (PDE)
gate2020-ce-2
partial-differential-equation
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2
GATE2020 CE-2-39
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by $ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \sin nx$ The value of $a_0$(round off to two decimal places), is ________.
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by$$ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \si...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 12, 2021
Partial Differential Equation (PDE)
gate2020-ce-2
numerical-answers
partial-differential-equation
fourier-series
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–
0
votes
0
answers
3
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...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 12, 2021
Partial Differential Equation (PDE)
gate2020-ce-1
partial-differential-equation
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0
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0
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4
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 $\...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 12, 2021
Partial Differential Equation (PDE)
gate2019-ce-1
partial-differential-equation
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–
1
votes
0
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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...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
retagged
Mar 12, 2021
Partial Differential Equation (PDE)
gate2019-ce-1
partial-differential-equation
laplace-equation
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0
votes
1
answer
6
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...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
retagged
Mar 11, 2021
Partial Differential Equation (PDE)
gate2018-ce-1
partial-differential-equation
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–
0
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0
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7
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...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
edited
Mar 11, 2021
Partial Differential Equation (PDE)
gate2017-ce-2
ordinary-differential-equation
second-order-differential-equation
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0
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0
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8
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 ...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 11, 2021
Partial Differential Equation (PDE)
gate2017-ce-1
numerical-answers
partial-differential-equation
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0
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0
answers
9
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) ...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 11, 2021
Partial Differential Equation (PDE)
gate2016-ce-2
partial-differential-equation
fourier-series
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–
0
votes
0
answers
10
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 ...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 11, 2021
Partial Differential Equation (PDE)
gate2016-ce-1
partial-differential-equation
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–
0
votes
0
answers
11
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...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 11, 2021
Partial Differential Equation (PDE)
gate2016-ce-1
partial-differential-equation
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0
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0
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12
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} = ...
Lakshman Bhaiya
12.8k
points
Lakshman Bhaiya
recategorized
Mar 10, 2021
Partial Differential Equation (PDE)
gate2013-ce
numerical-answers
partial-differential-equation
laplace-equation
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