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Thread: why isn't this problem homogeneous?

  1. #1
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    why isn't this problem homogeneous?

    ok i have this problem:

    dy/dx = (-y+10)/(x+1)

    i see that it is separable and exact, but why isn't this problem homogeneous? isn't everything to the power of 1?

    in the next problem i have the same issue.

    dy/dx = 1/(x(x-y))

    i got this problem wrong as well. i was trying to say that it is a homogeneous equation but my book says its a Bernoulli equation? why
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by slapmaxwell1 View Post
    isn't everything to the power of 1?
    $\displaystyle -y+10=-y^1+10y^0$ .

    in the next problem i have the same issue. dy/dx = 1/(x(x-y))
    Your equation is equivalent to $\displaystyle x(x-y)dy-dx=0$ , then $\displaystyle x(x-y)$ is homogeneus of degree $\displaystyle 2$ and $\displaystyle -1$ is homogeneous of degree $\displaystyle 0$ so, the equation is not homogeneous.


    Fernando Revilla
    Last edited by FernandoRevilla; Feb 13th 2011 at 02:58 PM.
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  3. #3
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    If your differential equation is of the form

    $\displaystyle \dfrac{dy}{dx} = F\left(\dfrac{y}{x}\right)$

    for some $\displaystyle F$ then it's homogeneous. Neither of the two equations you give can be put in this form.
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