How to eliminate the first derivative from xy''+2y'+(n²)xy=sin(ωx)

[outhsakotad]

Homework Statement

xy''+2y'+(n^2)*x*y=sin(omega*x)

Hint: Eliminate the first derivative term

Homework Equations

The Attempt at a Solution

I have tried lots of substitutions, but none of them seems to work out. I don't really understand what the hint is getting at. For example, I've tried y'=ux, but then I don't know what to do with the y. I've tried y=ux, but that doesn't seem to help matters at all. And I've tried numerous other silly things that haven't worked out. I'm really out of ideas and stuck. Any little hints would be greatly appreciated.

 

[CompuChip]

You notice that xy'' + y' looks very much like the derivative of a product.

So I suggest you try playing around with u = xy' or x(y'²); and if that doesn't work maybe u = xy