I'm trying to plot d^2y/dx^2=-y.
I think that the way forward is to solve the equation to get one in terms of x and y (but maybe there is a better way?). This gives me the auxiliary quadratic
(m^2) -1=0, so m=ħi
So the complimentary function is of the form y=Acosx+Bsinx.
But now I am stuck... I don't know how to find the particular integral. I used the trial solution y=λxsinx but didn't get anywhere.