Question

Find the order and degree, if defined of the differential equation
${\left(\begin{array}{c}\frac{d^{2}y}{d{x}^2}\end{array}\right)}^3+{\left(\begin{array}{c}\frac{dy}{dx}\end{array}\right)}^2+\sin \frac{dy}{dx}+1=0$.

Answer 1

Order is maximum number of times $y$ is differentiated in above differential equation.

Hence order $=2$ as $\frac{d^{2}y}{d{x}^2}$

Degree is the power of highest order $=3$ as ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3$