This is a second-order ODE since the highest order derivative is 2 (from [tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}[/tex]).
It's not linear because it doesn't take the form
[tex]F\left(\dfrac{\mathrm d^2y}{\mathrm dx^2},\dfrac{\mathrm dy}{\mathrm dx},y,x\right)=0\iff f_2(x)\dfrac{\mathrm d^2y}{\mathrm dx^2}+f_1(x)\dfrac{\mathrm dy}{\mathrm dx}+f_0(x)y+g(x)=0[/tex]
and it's not possible to rewrite it as such.
