I have the following equation:
$$\frac{dx}{dt}+x=4\sin(t)$$
For solving, I find the homogenous part as: $$f(h)=C*e^{-t}$$
Then finding $f(a)$ and $df(a)$: $$f(a)=4A\sin(t)+4B\cos(t)$$ $$df(a)=4A\cos(t)-4B\sin(t)$$
Substituting in orginal equation:
$$4A\cos(t)-4B\sin(t)+4A\sin(t)+4B\cos(t)=4\sin(t)$$
I have to find numerical values of $A$ and $B$ but I absoloutly have no idea how can I solve this, I am also not sure if the steps I did are correct or not. Would somone please help with this equation?
The final answer should be substituted in: $$x=f(h)+f(a)$$