The problem: $$y=3x^2 + sin (2x)$$; write down a 2nd order differential equation involving only d^2x/dy^2, functions of x and y, and constants.

Is this just asking for the second differential of the function i.e. $$6-4sin(2x)$$?

Question

The problem: $$y=3x^2 + sin (2x)$$; write down a 2nd order differential equation involving only d^2x/dy^2, functions of x and y, and constants.

Is this just asking for the second differential of the function i.e. $$6-4sin(2x)$$?

kinggeorge · Answer

My understanding is that it wants you to find an equation relating $y=3x^2+\sin(2x)$ and $y''=6-4\sin(2x)$. This equation should ideally be in the form$$f(x)y''+g(x)y=h(x)$$ where $f,g,h$ are functions of $x$.

kinggeorge · Answer

It would be even better if you could manipulate the functions so that $h(x)=0$.