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Homework Help: ODE- not sure if this is correct

  1. Jun 29, 2011 #1
    The problem is :

    (y*e^(2xy) +x) + [ b* x*e^(2xy) ] y' =0. Find b so the equation is exact and solve.

    I found b=1 and worked the problem to (1/2)e^(2xy) + (x^2/2)e^(2xy) + h(y); where I found h(y) to be simply c.

    The answer in the text states that e^(2xy) + x^2 =c

    Would I be incorrect to multiply [ (1/2)e^(2xy) + (x^2/2)e^(2xy) = -c ] by 2 to arrive at the answer since c is an arbitrary constant?

  2. jcsd
  3. Jun 29, 2011 #2
    I believe you are correct in multiplying through that way, absorbing the factor of 2 into the constant. However, it still will not give you the answer the text gives because you will now have e^(2xy)+x^2 e^(2xy)=c, where as the text gives e^(2xy)+x^2=c.
  4. Jun 29, 2011 #3
    Thanks. My mistake, the second term is (x^2/2) , not (x^2/2)e^(2xy)
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