I am not a mathematician, so excuse if my question is silly or badly stated. I have the following problem. I have 2 conditions on two unknown continuously differentiable functions:
$$A(t)=\frac{1}{B(t)}+C \\ B(t)=D-A(t)-\int_0^t A(\tau) d\tau.$$
C and D are constants. I also know $A(0)$ and $B(0)$. I am looking for a way to get the value of $A(t)$ and $B(t)$ for small $t>0$. So far I have a numerical solution, but that involves a lot of interpolation and I don't think it is very good.
I was wondering if there is some way to get an analytic solution for this problem. I don't expect you to solve the problem for me, I'm willing to learn and I'd be very grateful if you could point me towards possible readings.
Thanks in advance.