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Homework Help: Differential equation

  1. Mar 19, 2013 #1

    I need help with the following differential equation:

    [tex](1-\frac{gh}{c^2}) A(u) - \frac{h^2}{3} A''(u) - \frac{3}{2h} A(u)^2 =0 [/tex]

    with [tex]g,h,c=constant[/tex]

    the answer has a [tex] \sech^2 [/tex] with [tex]A(0)=A_0[/tex] and [tex]A'(0)=0[/tex]

  2. jcsd
  3. Mar 19, 2013 #2


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    Science Advisor
    Homework Helper

    hello alejandrito29! :smile:

    that's A'' = pA - qA2 with p and q constant

    start by multiplying both sides by A', and then integrating :wink:
  4. Mar 19, 2013 #3
    differential equation1

    i have the differential equation

    [tex] A''=p A - q A^2 [/tex]

    i multiplying by A' both sides then

    [tex] A' A''=p A A' - q A^2A' [/tex] then

    [tex] (\frac{1}{2}(A')^2)'=\frac{p}{2} (A^2)' - \frac{q}{3} (A^3)' [/tex]
    then i integer and:

    [tex] (\frac{1}{2}(A')^2)=\frac{p}{2} (A^2) - \frac{q}{3} (A^3) [/tex]

    but i write in maple this differential equation and i dont obtain the solution. This solution must have of the way [tex] A(x)=k_1 sech ^2 (k_2 x) [/tex]

    help please
    Last edited: Mar 19, 2013
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