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Math Help - Solve the differential equation (show steps!)

  1. #1
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    Solve the differential equation (show steps!)

    I came across this differential equation while trying to solve a specific parametric equation for a parabola. The equation is:

    y*y''+(y')^2=0

    Wolfram|Alpha suggests the square root function, but I want to know the mathematics that derive that result. The furthest I've gotten in my personal study of differential equations is the Wronskian Method for Non-homogeneous Linear Differential Equations of the Second Order.
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  2. #2
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    Quote Originally Posted by pikalax1 View Post
    I came across this differential equation while trying to solve a specific parametric equation for a parabola. The equation is:

    y*y''+(y')^2=0

    Wolfram|Alpha suggests the square root function, but I want to know the mathematics that derive that result. The furthest I've gotten in my personal study of differential equations is the Wronskian Method for Non-homogeneous Linear Differential Equations of the Second Order.
    The left side of that equation is just the derivative of yy'. So you can integrate the equation once to get yy' = const. Then integrate again to get y^2 = ax+b. So the general solution is y = \pm\sqrt{ax+b}.
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  3. #3
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    Thank you.
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