Hey everyone, I need help understanding solving this equation as it deals with an input function that is discontinuous, which I don't know how to handle.

$\displaystyle g(x) =sin x$ for $\displaystyle 0 \le x \le \frac{\pi}{2}$

$\displaystyle g(x)=0$ for $\displaystyle x > \frac{\pi}{2}$

Solve $\displaystyle y''+4y=g(x)$

The two intervals:

$\displaystyle y'' +4y = sin (x)$ for $\displaystyle 0 \le x \le \frac{\pi}{2}$

and

$\displaystyle y'' +4y = 0$ for $\displaystyle x > \frac{\pi}{2}$

with $\displaystyle y(0)= 1$ and $\displaystyle y'(0)=2$

Can anyone help me?

Thanks