Question

Find order and degree of the following differential equation:
$5{\left(\frac{d^{2}y}{d{x}^2}\right)}^4-{\left(\frac{dy}{dx}\right)}^2+2y=\sin x$

Answer 1

$5{\left(\frac{d^{2}y}{d{x}^2}\right)}^4-{\left(\frac{dy}{dx}\right)}^2+2y=\sin x$

order $=2$ ($\Rightarrow \frac{d^{2}y}{d{x}^2}$ is the highest order of differentiation)

degree $=$ degree of the highest order

$=$ degree of $\frac{d^{2}y}{d{x}^2}=4$

(degree,order)$=(4,2)$