Question

If $y=a[x+\sqrt{x^2+1}{]}^n+b[x-\sqrt{x^2+1}{]}^{-n}$ then$(x^2-1)\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}-n^{2}y=0$

• A. True
• B. False

Answer 1

The correct option is B False

This is the form of legendre differential equation

The cofficeient of $\frac{d^{2}y}{d{x}^2}$ can not be $(x^2-1)$

It is of the form $(1+x^2)\frac{d^y}{d{x}^2}+x\frac{dy}{dx}-n^{2}y=0$

So given Equation is fals