x'(t)=-ax(t)

y'(t)=ax(t)-by(t)

The question is to find x(t) and y(t).

I managed to find x(t):

x(t)=exp(-at)

but I have trouble finding y(t).

I know the solution is y(t)=(a/(b-a)) (exp(-at)-exp(-bt))

I would appreciate very much your help. Thank you!