Inhomogenous differential equation of second order

[Chromosom]

Homework Statement

$$y^{\prime\prime}+y=\frac{1}{\sin x}$$

Homework Equations

The Attempt at a Solution

I solved the homogenous equation: $$y=C_1\sin x+C_2\cos x$$, and then I tried to use method of variable the constant. But the equation system is rather hard. Do you know any other method that can be used here?

 

[ehild]

The method of variation of constants works well. Show what you have done.

ehild

 

[Chromosom]

Yeah, it does. Thanks for your answer. I started to calculate it and I got it. For future visitors: you must multiplicate first equation by $$\cos x$$ and second by $$\sin x$$ and try to reduce it.