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Thread: homogeneous differential equation->separation of variables

  1. #1
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    homogeneous differential equation->separation of variables

    Let $\displaystyle M(x,y)dx+N(x,y)dy=0$ - be a homogeneous differential equation.
    Prove that by the sustitution of:
    $\displaystyle x=rcos\theta
    y=rsin\theta
    $
    it can be solved by Separation of Variables method.

    Thanks a lot.
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  2. #2
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    Quote Originally Posted by sinichko View Post
    Let $\displaystyle M(x,y)dx+N(x,y)dy=0$ - be a homogeneous differential equation.
    Prove that by the sustitution of:
    $\displaystyle x=rcos\theta
    y=rsin\theta
    $
    it can be solved by Separation of Variables method.

    Thanks a lot.

    $\displaystyle dx=-rsin\theta d\theta$ and $\displaystyle dy=rcos\theta d\theta$

    $\displaystyle
    M(rcos,rsin)(-rsin\theta d\theta)+N(rcos,rsin)(rcos\theta d\theta)=0
    $
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