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Math Help - How to solve dy/dx=x^2-sqrt(y)

  1. #1
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    How to solve dy/dx=x^2-sqrt(y)

    How to solve this differential equation dy/dx=x^2-sqrt(y)? Thanks.
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  2. #2
    A Plied Mathematician
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    Re: How to solve dy/dx=x^2-sqrt(y)

    I only have two ideas, neither one of which is going to be terribly good news. The first idea is to attempt a series solution. Before doing so, you might want to transform the equation thus: let u=\sqrt{y}, implying that u^{2}=y. Then 2uu'=y', and the DE becomes

    2uu'=x^{2}-u.

    It might be easier to work with the series solution in this format than with the y equation.

    The second idea is to solve the DE numerically. You'll need an initial condition to pull that off.

    What is the context for this DE? Does it arise from a physical problem?
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