The partial differential equation- 2u- t2-C2 - 2u- x2- 2u- y2 -0 - where c - 0 is known as

(i) Wave equation ∂ ^2u∂ t^2=C^2 ( ∂ ^2u∂ x^2+∂ ^2∂ y^2 ) (ii) Laplace equation nbsp; ∇^2u=∂ ^2u/∂ x^2+∂ ^2u/∂ y^2=0 (iii) Poission equation nbsp;∇^2u = ...

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Engineering Mathematics

Solution of Two dimensional Laplace equation.

The partial d...

Question

The partial differential equation

$\frac{\partial^{2} u}{\partial t^{2}} - C^{2} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}}) = 0$ ; where c $\neq$ 0 is known as

wave equation

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laplace equation

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heat equation

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poission's equation

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Solution

The correct option is A wave equation
(i) Wave equation

$\frac{\partial^{2} u}{\partial t^{2}} = C^{2} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}})$

(ii) Laplace equation

$\nabla^{2} u = \frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} = 0$

(iii) Poission equation

$\nabla^{2} u = f$

(iv) Heat equation

$\frac{\partial u}{\partial t} - α (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} + \frac{\partial^{2} u}{\partial z^{2}}) = 0$

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Similar questions

Q. The solution of the following partial differential equation

\frac{\partial^{2} u}{\partial x^{2}} = 9 \frac{\partial^{2} u}{\partial y^{2}}

Q. The partial differential equation

\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} = \frac{\partial^{2} u}{\partial x^{2}}

is a

Q. The solution at

x = 1, t = 1

of the partial differential equation

\frac{\partial^{2} u}{\partial x^{2}} = 25 \frac{\partial^{2} u}{\partial t^{2}}

subject to initial conditions of

u (0) = 3 x

and

\frac{\partial u}{\partial t} (0) = 3

Q. The solution of the partial differential equation

\frac{\partial u}{\partial t} = α \frac{\partial^{2} u}{\partial x^{2}}

is of the form

Q. If

u = f (r)

, where

r^{2} = x^{2} + y^{2}

then

(\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}}) =

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The partial differential equation ∂2u∂t2−C2(∂2u∂x2+∂2u∂y2)=0 ; where c ≠ 0 is known as

The correct option is A wave equation(i) Wave equation ∂2u∂t2=C2(∂2u∂x2+∂2∂y2) (ii) Laplace equation ∇2u=∂2u∂x2+∂2u∂y2=0 (iii) Poission equation ∇2u=f (iv) Heat equation ∂u∂t−α(∂2u∂x2+∂2u∂y2+∂2u∂z2)=0

The partial differential equation

$\frac{\partial^{2} u}{\partial t^{2}} - C^{2} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}}) = 0$ ; where c $\neq$ 0 is known as