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Math Help - how do i solve this second order differential equation?

  1. #1
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    how do i solve this second order differential equation?

    please could someone explain how to solve this second order differential equation. I know how to do it when it has a first order term as well, but in this case that term equals zero. so need to solve this...

    1/2f''(x)y^2=0

    Thanks
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  2. #2
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    Quote Originally Posted by willowtree View Post
    please could someone explain how to solve this second order differential equation. I know how to do it when it has a first order term as well, but in this case that term equals zero. so need to solve this...

    1/2f''(x)y^2=0

    Thanks
    I take it that this is actually

    \frac{1}{2}\cdot \frac{d^2y}{dx^2}\cdot y^2 = 0.


    It should be easy to see that either \frac{d^2y}{dx^2} = 0 or y^2 = 0.


    Case 1:

    \frac{d^2y}{dx^2} = 0

    \frac{dy}{dx} = C_1

    y = C_1x + C_2.


    Case 2:

    y^2 = 0

    y = 0.
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