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Math Help - bernoulli equation

  1. #1
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    Angry bernoulli equation

    dy/dx - 2y = (4x)/(y^1/2)

    I assumed that u = y^1/2 would be the proper substitution, but it didn't seem like things were going in the right direction.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by markmil2002 View Post
    dy/dx - 2y = (4x)/(y^1/2)

    I assumed that u = y^1/2 would be the proper substitution, but it didn't seem like things were going in the right direction.
    Note that \frac{\,dy}{\,dx}-2y=\frac{4x}{y^{\frac{1}{2}}}\implies \frac{\,dy}{\,dx}-2y=4xy^{-\frac{1}{2}},

    The substitution is of the form z=y^{1-n}, so we see in this case, the proper substitution would be z=y^{\frac{3}{2}}

    Try to take it from here. This should lead you to the desired result.

    See here for an example on how to solve a Bernoulli equation (see post #3)

    I hope this helps!

    --Chris
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