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Math Help - Second Order ODE: Exact Equations

  1. #1
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    Second Order ODE: Exact Equations

    The problem is
    y+(x+2xy^2)dy/dx=0
    Im trying to find an integrating factor to make this exact. To get the integrating factor u:
    du/dy=u[(Nx-My)/M ]= u(1+2y2-1)/y=2y*u
    u=e^(2y)
    If I multiply it by My and Nx, they don't equal.
    Then my equation still isnt exact. What did I do wrong? I feel like Ive been over this 20 times already.
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  2. #2
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    I have a question. Fom what you have

    y +\left(x + 2xy^2\right) \dfrac{dy}{dx} = 0. Isn't this ODE spearable?
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  3. #3
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    Quote Originally Posted by sweetscissor View Post
    The problem is
    y+(x+2xy^2)dy/dx=0
    Im trying to find an integrating factor to make this exact. To get the integrating factor u:
    du/dy=u[(Nx-My)/M ]= u(1+2y2-1)/y=2y*u
    u=e^(2y)
    If I multiply it by My and Nx, they don't equal.
    Then my equation still isnt exact. What did I do wrong? I feel like Ive been over this 20 times already.
    To comment on what you've done - check your integration

    \left(\int 2y\,dy = y^2\right)
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