Question

Find the order and degree of ${\left[\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^3\right]}^{\frac{6}{5}}=6y$.

Answer 1

We have, ${\left[\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^3\right]}^{\frac{6}{5}}=6y$.

take $5^{th}$ power both sides,

${\left[\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^3\right]}^6=(6y{)}^5$.

So degree $=6$

and order $=2$