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Math Help - determine a region in the xy plane...

  1. #1
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    determine a region in the xy plane...

    ok so im supposed to determine a region in the xy plane that would have a unique solution whose graph passes through a point in the region. (x+3y)y' = 2x - y

    im not sure where to start this problem. am i supposed to find a point that satisfies the equation? any help would be appreciated.

    thanks
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  2. #2
    Member SENTINEL4's Avatar
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    Maybe you should solve the differential equation at the beginning??
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by slapmaxwell1 View Post
    ok so im supposed to determine a region in the xy plane that would have a unique solution whose graph passes through a point in the region. (x+3y)y' = 2x - y

    Consider the domain:

    D=\left\{{(x,y)\in \mathbb{R}^2:x+3y\neq 0}\right\}

    and

    y'=f(x,y)=\dfrac{2x-y}{x+3y}

    We have:

    \rightarrow{\mathbb{R}}" alt="(i)\quad f\rightarrow{\mathbb{R}}" /> is continuous.


    (ii)\quad \dfrac{{\partial f}}{{\partial y}}\in\mathcal{C}^1(D)

    Now, use a well known existence and uniqueness theorem.


    Fernando Revilla
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  4. #4
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    thanks fernando. i went back and redid the problem. and yes i looked at where the domain would not exist and used that to help me to find my domain.
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