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Help Finishing ODE

  1. Apr 9, 2006 #1
    I need help completing this problem:

    y'' - 4k^2 y^2 = 0, y(0) = 2, y'(0) = 4k, k > 0 and fixed constant

    Let v = y'

    dv/dx = dv/dy * dy/dx = dv/dy * v

    dv/dy * v - 3k^2 y^2 = 0

    Integral( v dv ) = Integral( 3k^2 y^2 )

    v^2 = 2k^2 y^3 + C0

    v(0) = 4k ==> C0 = 16k^2

    dy/dx = sqrt( 2k^2 y^3 + 16k^2 )

    I think this is separable, but I can't do the integral, so I think I messed up somewhere.
     
  2. jcsd
  3. Apr 9, 2006 #2
    Your equation for v(0) is wrong, since v(0)=4k ==> 16k^2 = 2k^2*y(0)^3 + C0 = 2k^2 * 8 * C0 ==> C0 = 0. This makes the separable equation easier.
     
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