
Need help solving
Hello, I am having trouble solving the following problem. I'll spare you the derivations but I have 3 equations:
1) $\displaystyle \.{a(t,s)} = (r(t)v)*a(t,s)c(t,s)+w(t) $
2) $\displaystyle \lim_{t \to +\infty} e^{\frac{1}{ts}\int_s^{t}{r(y)dyv}} * a(t,s)=0 $
3) $\displaystyle \.{c(t,s)}=c(t,s)*(r(t)p) $
where p and v are constants And r and w do not depend on s.
I need to show that:
$\displaystyle c(t,s) = (p+v)*(a(t,s) + W(t)) $
where $\displaystyle W(t)=\int_t^{\infty}{e^{\frac{1}{xt}\int_t^{x}{r(y)dyv}}*w(x)dx $