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Thread: Differential Equation Problem

  1. #1
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    Differential Equation Problem

    (x+y) * (dy/dx) = (x-y)

    the given answer is y^2-2xy-x^2 = C

    The problem is in a section of the textbook where substitution methods are taught. That is, making a subsitution where v = some term containing the variables x and y. Then solving the substitution equation so that y = some term containing the variables x and v. Taking the derivative of that term so dy/dx can be substituted for. Then the next step would be to separate the variables x and v. integrate, and lastly you substutite x and y back in for v to gain your solution to the Diff EQN.

    Problem is, I can't do it.

    Help is much appreciated!

    JB
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  2. #2
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    Quote Originally Posted by jblorien View Post
    (x+y) * (dy/dx) = (x-y)

    the given answer is y^2-2xy-x^2 = C
    First rewrite your equation as follows:

    $\displaystyle \frac{{dy}}
    {{dx}} = \frac{{x - y}}
    {{x + y}}.$

    Now multiply top & bottom by $\displaystyle \frac1x,$

    $\displaystyle \frac{{dy}}
    {{dx}} = \frac{{1 - \dfrac{y}
    {x}}}
    {{1 + \dfrac{y}
    {x}}}.$

    Now it remains to substitute $\displaystyle y=ux.$
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  3. #3
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    Thank you
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