Question

Find the order and degree of : $\sqrt[3]{3\frac{d^{2}y}{d{x}^2}}=\sqrt{\frac{dy}{dx}}$.

Answer 1

$3\sqrt{\frac{d^{2}y}{d{x}^2}}=\sqrt{\frac{dy}{dx}}$

${\left(\frac{d^{2}y}{d{x}^2}\right)}^{3/2}={\left(\frac{dy}{dx}\right)}^{1/2}$

squaring on both sides

${\left(\frac{d^{2}y}{d{x}^2}\right)}^3-\left(\frac{dy}{dx}\right)=0$

In this equation order $=2$

degree $=3$