Question

Find the order and degree of the differential equation:

$\frac{d^{2}y}{d{x}^2}+y=\sqrt{1+\frac{dy}{dx}}$.

Answer 1

The given differential equation

$\frac{d^{2}y}{d{x}^2}+y=\sqrt{1+\frac{dy}{dx}}$

can be expressed as

${(\frac{d^{2}y}{d{x}^2}+y)}^2=1+\frac{dy}{dx}$.

It is clear that second order term is involved in the equation which is the highest order term in the equation so order of the differential equation is $2$ and highest power of the highest ordered term in the equation is $2$ so degree of the differential equation is $2$.