Question

The degree and order of differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^2={(y+\frac{dy}{dx})}^{\frac{1}{2}}$ is which of the following?

Answer 1

We have,

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

On squaring both sides, we get

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

So,

Order $=2$

Degree $=4$

Hence, this is the answer.