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Math Help - Differential equation

  1. #1
    Junior Member
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    Differential equation

    How to solve this differential equation
    \left(\frac{dy}{dx}\right)^{4}+B\left(\frac{dy}{dx  }\right)^{3}+C=0
    where B and C are constants.
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  2. #2
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    Re: Differential equation

    Quote Originally Posted by JulieK View Post
    How to solve this differential equation
    \left(\frac{dy}{dx}\right)^{4}+B\left(\frac{dy}{dx  }\right)^{3}+C=0
    where B and C are constants.
    let dy/dx = u
    solve that nasty 4th order polynomial equation you now have, for u. (it's not pretty)
    Note that u is just a constant. (up to 4 constants actually)

    Integrate u over x to obtain y(x) = u x + const. This is actually up to 4 separate solutions as there are up to 4 distinct roots of your polynomial.
    The differential equation is satisfied for all the u's.

    did you maybe mean d4y/dx4 + B d3y/dx3 + C = 0 ?
    Last edited by romsek; November 29th 2013 at 01:52 PM.
    Thanks from topsquark
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