3√(1+(dy/dx)^2) = d^2y/dx^2

Question

Determine the order and degree of the following differential equation:

\(\sqrt[3]{1+\left(\frac{dy}{dx}\right)^2}\) = \(\frac{d^2y}{dx^2}\)

3√(1+(dy/dx)²) = d²y/dx²

Answer 1

The given D.E. is \(\sqrt[3]{1+\left(\frac{dy}{dx}\right)^2}\) = \(\frac{d^2y}{dx^2}\)

On cubing both sides, we get

This D.E. has highest order derivative \(\frac{d^2y}{dx^2}\) with power 3.

∴ the given D.E. is of order 2 and degree 3.