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 $\ne$ 0 is known as

• A. wave equation
• B. laplace equation
• C. heat equation
• D. poission's equation

Answer 1

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

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