Determine order and degree(if defined) of differential equation

$y^{\prime \prime}+\left(y^{\prime}\right)^{2}+2 y=0$

The highest order derivative present in the differential equation is $y^{\prime \prime}$. Therefore, its order is two.

The given differential equation is a polynomial equation in $y^{\prime \prime}$ and $y^{\prime}$ and the highest power raised to $y^{\prime \prime}$ is one.

Hence, its degree is one.