How do we solve d^2/dx^2 + y = sinx*sin 2x

Question

How do we simplify the RHS to the form sin(ax+b) ?

Answer 1

I do not understand your leftside
but sin 2x = 2 sin x cos x
so
sin x sin 2x = 2 sin^2 x cos x
so you have
d^2/dx^2 + y = 2 sin^2 x cos x

well d/dx ( sin^3 x )= 3 sin^2x cos x
so (2/3) d/dx (sin^3 x) =2 sin^2 x cos x (oh my)

d^2/dx^2 + y = (2/3) d/dx (sin^3 x)
maybe that might help

Answer 2

That's d^2y/dx^2 + y = sinx*sin 2x

Could you please explain how to get the particular integral of that?

Answer 3

There is no way to simplify sinx sin2x to sin(ax+b)
just a glance at the graph will tell you that much. It is not a simple sinusoidal curve.