Linear, non linear and homeogenous and non homeogenous

[Taylor_1989]

Homework Statement

Hi guys, I am having a bit of trouble with this question:

S2. It the linear non linear and homogeneous parts. I think it is a linear equation, as I always think dy/dx (y)=H(x), but is there a way to show this, also for non linear cases. I believe the second part to this question my ans in Inhomeogenous, but once again is there a mathmatical way to show this. I know its not asking for that in the question but for future ref. Also I is omega a constant in this?

Homework Equations

The Attempt at a Solution

 

[andrewkirk]

For S2 to be linear, we must be able to express it in the form $Ly=f(t)$ for some linear differential operator $L$ and function $f$. Can you do that?

Re homogeneity: first express the equation in the form given here. Having done that, what are the functions $M(y,t)$ and $N(y,t)$? Are they both homogeneous?