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How to integrate complicated differential equation

  1. Jun 19, 2011 #1
    1. The problem statement, all variables and given/known data

    I need to integrate ∫ -y3ey2/2

    2. Relevant equations

    Integration by parts

    3. The attempt at a solution

    I have tried several times, I am unable to find the correct solution, which is:

    -yey2/2 + 2ey2/2 + c
     
  2. jcsd
  3. Jun 19, 2011 #2
    I think you can use u substitution. Let u = y^2, du = 2y. If you factor that y^3 at y^2 * y it should work. You might have to also do integration by parts afterwards.
     
  4. Jun 19, 2011 #3
    Try a u-substitution.
     
  5. Jun 20, 2011 #4

    hunt_mat

    User Avatar
    Homework Helper

    Here is a possibly slicker method, calculate:
    [tex]
    \int ye^{ay^{2}}dy
    [/tex]
    This should be very straight forward, the result should be a function of a, all you do now is differentiate the result with respect to a and then set a=1/2.
     
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