Question

Prove the wave equation :-

${ \displaystyle { \dfrac{{\partial ² u}}{{\partial t²}} = c² × { \dfrac{{\partial ² u}}{{\partial x²}}}}}$

It is to be understood that the symbols have their usual meanings ! ​

Answer 1

Answer:

Given equation,

Compare the given equation with the following general equation

Hence we get,

A = 1, B = 3, C = 1

Put value of A,B, and C in the following equation

B2 – 4AC

∴ B2 – 4AC = 32 – (4× 1 × 1) = 5

We can see B2 – 4AC is greater than Zero, i.e

B2 – 4AC > 0

Hence the given partial differential equation is Hyperbolic