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Seperable differential equations question

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve the differential equation dy/dx = 3x2(1+y2)3/2

    2. Relevant equations

    3. The attempt at a solution
    So far this is what I have (I'm almost finished) -

    ∫dy/(1+y)3/2 = ∫3x2 dx
    Let y = tan(u) , dy = sec2(u)
    Then (1+y2)3/2 = (tan2(u)+1)3/2 = sec3(u) and u = tan-1(y)
    ∫cos(u)du = ∫3x2dx
    sin(u)+c = x3+c
    sin(tan-1(y)) = x3+C

    One question here, how do I simplify the left-hand side? I seem to have forgotten. Thanks!
  2. jcsd
  3. Jan 30, 2012 #2


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    Draw a right triangle with an angle 'a' that satisfies tan(a)=y. Work out the hypotenuse. Now find sin(a).
  4. Jan 30, 2012 #3
    thank you!
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