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}{t-s}\int_s^{t}{r(y)dy-v}} * 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}{x-t}\int_t^{x}{r(y)dy-v}}*w(x)dx $