Differential Equations and Linear Algebra (4th Edition)

To the left of the equal sign, there is a $\frac{1}{y'}$ coefficient. This is not allowed in the linear equation, whose form is $a_o(x)y^{(n)}+a_1(x)y^{(n-1)}+...+a_n(x)y=F(x)$. Therefore, the equation is nonlinear.