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Math Help - Integrating Factor

  1. #1
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    Integrating Factor

    I'm doing Tenenbaum's ODE page 91, problem 16, can't see what's going on. We have 3(x+y)^{2}dx + x(3y + 2x)dy = 0 \Rightarrow \frac{d}{dy}P(x,y) = 6(x+y) \text{and} \frac{d}{dx}Q(x,y) = 3y + 4x \Rightarrow I want to find an integrating factor by finding one of the forms in which I can divide the difference of these, 2x + 3y, by yQ - xP (or there are formulae if this is off by a factor of -1). Or I want yQ+xP to divide 2x + 3y times a factor of x^{2} or y^{2}.

    But yQ - xP = -x^{2}(4y + 3x) (grrrrr! so close! )

    And yQ + xP only factors into an x and something bad.

    So... I got nothing.
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  2. #2
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    GAAAH, I see it now. Nevermind.
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