The sum of the order and degree of the differential equation $\frac{d^2y}{dx^2}+\sqrt{\frac{dy}{dx}}+(1+x)=0$ is :

4

The correct answer is Option (2) → 4

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

Squaring both side

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

order = 2, degree = 2

So $2+2=4$