Answer
Nonlinear.
Work Step by Step
There is a $y^2$ term to the right of the equal sign, so some of the $y$ terms are raised to a power other than $1$ and the equation does not fit the linear differential $a_o(x)y^{(n)}+a_1(x)y^{(n-1)}+...+a_n(x)y=F(x)$.
