# Math Help - Separable differential equation

1. ## Separable differential equation [Solved]

Hey I have been trying to figure out this equation for a while now:

Solve for u & the initial conditions of u(0)=9

du/dt=e^(5u+10t)

I have tried taking the natural log of both sides to eliminate the e and isolate the 5u+10t but then the left side of the equation gives me a problem, since I don't know how to work with ln(du/dt). Any help on just solving for u would be fine, since using the initial conditions should not be a problem.

Thank you!

2. Remember that $e^{(5u+10t)}$ can be written as $e^{5u} e^{10t}$, this should help you out.

3. Thanks craig, it turned out to be correct.

The answer ended up being (including the initial conditions):

u=(-1/5)ln((-e^(10t)/2+1/(e^45)+(1/2)))