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Math Help - Separable differential equation

  1. #1
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    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!
    Last edited by Jewgro; March 24th 2010 at 05:07 PM.
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  2. #2
    Super Member craig's Avatar
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    Remember that e^{(5u+10t)} can be written as e^{5u} e^{10t}, this should help you out.
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  3. #3
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    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)))
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