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Math Help - Non-linear Differencial Equation

  1. #1
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    Non-linear Differencial Equation

    This one is my own, which supprizingly has a nice solution to it:

    y' = y^2
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  2. #2
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    Quote Originally Posted by ThePerfectHacker View Post
    This one is my own, which supprizingly has a nice solution to it:

    y' = y^2
    This is just a Bernoulli equation:

    Let z(x) = 1/y(x)

    Then y = 1/z ==> y' = -z'/z^2

    So
    -z'/z^2 = 1/z^2

    z' = -1

    z(x) = -x + C

    Thus
    y(x) = 1/(C - x)
    is the general solution.

    -Dan
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    Ha ha I forgot about that.
    I had a different idea.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Ha ha I forgot about that.
    I had a different idea.
    Well then, what's your idea? (I've heard there is more than one way to skin a cat...)

    -Dan
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    Quote Originally Posted by topsquark View Post
    Well then, what's your idea? (I've heard there is more than one way to skin a cat...)

    -Dan
    Power series solution.

    It really is quite elegant here.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Power series solution.

    It really is quite elegant here.
    Ah! I can see that.

    -Dan
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