Question

Degree of the differential equation $\frac{d^{2}y}{d{x}^2}={\{y+{\left(\frac{dy}{dx}\right)}^2\}}^{1/4}$ is

Answer 1

We have,
$\frac{d^{2}y}{d{x}^2}={\{1+{\left(\frac{dy}{dx}\right)}^2\}}^{1/4}$

To find the degree the differential equation must be polynomial equation $\Rightarrow {\left(\frac{d^{2}y}{{dx}^2}\right)}^4=1+{\left(\frac{dy}{dx}\right)}^2$

So, degree $=4$