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Math Help - Need help solving

  1. #1
    Member
    Joined
    Feb 2010
    Posts
    147

    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
    Last edited by southprkfan1; January 22nd 2011 at 12:05 PM.
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