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Homework Help: Something wrong? can't find my error.

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data

    x dy/dx -y = 2x^2 y, y(1)=1

    2. Relevant equations



    3. The attempt at a solution

    x dy/dx = y(2x^2 + 1)

    int 1/y dy = int (2x^2+1)/x dx

    int 1/y dy = int 2x dx + int 1/x dx

    ln y = x^2 + lnx + c

    y = exp(x^2 + c) + x and in this case initial condition doesn't work.

    please help. I can't find what went wrong.

    The answer turns out to be y = x exp(x^2-1).

    help~~
     
  2. jcsd
  3. Sep 1, 2010 #2

    Mark44

    Staff: Mentor

    Your error is in the line above. Since lny = x^2 + lnx + C, then y = e^(lnx + x^2 + C). Now think about the laws of exponents, particularly that a^(m + n) = a^m * a^n.
     
  4. Sep 1, 2010 #3

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [tex]e^{x^2+lnx+c}=e^{x^2}e^{lnx}e^c=xe^{x^2}e^c[/tex]

    You seem to have confused multiplication and addition for your last step
     
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