Question

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

Answer 1

The given equation is $xy\frac{d^{2}y}{d{x}^2}+x{\left(\frac{dy}{dx}\right)}^2-y\frac{dy}{dx}=0$

Order and degree of a differential equation is defined as the order and power of the highest order derivative respectively.

Since the highest order derivative in the given equation is $\frac{d^{2}y}{d{x}^2}$, the order of given equation is $2$.

Since the highest order derivative in the given equation is $\frac{d^{2}y}{d{x}^2}$ and the highest degree of it is $1$, the degree of the given equation will be $1$

Hence, the order is $2$ and degree is $1$.