Degree of the differential equation $\frac{d^2y}{dx^2}+3(\frac{dy}{dx})^{\frac{1}{2}}=y^2+e^x$ is:

2

$\frac{d^2y}{dx^2}+3[\frac{dy}{dx}]^{\frac{1}{2}}=y^2+e^x$

removing fractional power from derivative 

so $\frac{d^2y}{dx^2}-y^2-e^x=-3[\frac{dy}{dx}]^{\frac{1}{2}}$

squaring both sides

$(\frac{d^2y}{dx^2})^2+y^4+e^{2x}-2\frac{d^2y}{dx^2}×y^2+2y^2e^x-2e^x\frac{d^2y}{dx^2}=9\frac{dy}{dx}$

degree = 2