Taking the fact that $x(0)=0$ I tried solving it using Laplace transformations and I reached that $A=\frac{1}{a}$ and you also have $\sin$ and $\cos$ on the solution I also tried to use the trigonometry identitie: $\cos(\alpha-\beta)=\cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)$ to get something similar and I reached that $B$ could be something like $\frac{1}{a^2+b^2}$ but it is wrong.
The answer for $A$ is good but $B$ any of my alternatives still wrong.