# Need help solving

• January 22nd 2011, 10:03 AM
southprkfan1
Need help solving
Hello, I am having trouble solving the following problem. I'll spare you the derivations but I have 3 equations:

1) $\.{a(t,s)} = (r(t)-v)*a(t,s)-c(t,s)+w(t)$

2) $\lim_{t \to +\infty} e^{\frac{-1}{t-s}\int_s^{t}{r(y)dy-v}} * a(t,s)=0$

3) $\.{c(t,s)}=c(t,s)*(r(t)-p)$

where p and v are constants And r and w do not depend on s.

I need to show that:

$c(t,s) = (p+v)*(a(t,s) + W(t))$

where $W(t)=\int_t^{\infty}{e^{\frac{-1}{x-t}\int_t^{x}{r(y)dy-v}}*w(x)dx$