Having trouble solving this differential equation:

$\displaystyle

\frac{\partial \Phi}{\partial x} - K\Phi(x) = -g(x)

$

The answer I have so far is:

$\displaystyle

\int_0^{\tau} \frac{\partial \Phi}{\partial x} dx = K\int_0^{\tau}\Phi(x)dx - \int_0^{\tau}g(x) dx

$

$\displaystyle

\Phi = K\int_0^{\tau} \Phi (x)dx - \int_0^{\tau} g(x) dx

$

However it seems strange that I get an expression for $\displaystyle \Phi$ in terms of an integral of $\displaystyle \Phi$.

Any help would be much appreciated.

P.S. mr fantastic, seeing as this message had to come all the way from Neverland it took a little time to arrive fully! lol!