Question

For each of the differential equation given below, indicate its order and degree (if defined).
(i) $\frac{d^{2}y}{d{x}^2}+5x{\left(\frac{dy}{dx}\right)}^2-6y=\log x$

(ii) ${\left(\frac{dy}{dx}\right)}^3-4{\left(\frac{dy}{dx}\right)}^2+7y=\sin x$

(iii) $\frac{d^{4}y}{d{x}^4}-\sin \left(\frac{d^{3}y}{d{x}^3}\right)=0$

Answer 1

Differential equations are often classified with respect to order.

The order of a differential equation is the order of the highest order derivative present in the equation.
The degree of a differential equation is the power of the highest order derivative in the equation.
$i)$ order is 2 and degree is 1.
$ii)$ order is 1 and degree is 3.
$iii)$ order is 4 but degree is not defined because it is not polynomial.