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Math Help - Existence and Uniqueness Th.

  1. #1
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    Existence and Uniqueness Th.

    Discuss the application of the existence and uniqueness theorem to the initial value problem

    y' = (x - y)/(x + 3y) ; y(0) = -1
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  2. #2
    MHF Contributor chisigma's Avatar
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    The equation is written in 'normal fashion'...

    y^{'}= f(x,y) , y(x_{0})=y_{0} (1)

    ... where...

    f(x,y)= \frac{x-y}{x+3\cdot y} , x_{0}=0 , y_{0}= -1

    The partial derivative of f(*,*) respect to y is...

    f_{y}^{'}= - \frac {4\cdot x}{(x+3y)^{2}}

    Both f(*,*) and f_{y}^{'}(*,*) are continous in [0,1] so that does exist one and only one solution of (1) crossing that point...

    Kind regards

    \chi \sigma
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  3. #3
    MHF Contributor

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    My first thought would be "What IS the existence and uniqueness theorem?" What exactly does it say?
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