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Math Help - differential equation help

  1. #1
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    differential equation help

    du/dt = -u^2(t^3-t)

    Find the general solution to the above differential equation. Write the answer in a form such that its numerator is 1 and its integration constant is C

    Find the particular solution of the above differential equation that satisfies the condition u=4 at t=0.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by derekjonathon View Post
    du/dt = -u^2(t^3-t)

    Find the general solution to the above differential equation. Write the answer in a form such that its numerator is 1 and its integration constant is C

    Find the particular solution of the above differential equation that satisfies the condition u=4 at t=0.
    \int-u^{-2}\,du=\int t^3-t\,dt\implies \frac{1}{u}=\frac{t^4}{4}-\frac{t^2}{2}+C

    The rest is just algebra.
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