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Solving ode with complex numbers

  1. Mar 25, 2014 #1
    I want to solve [itex] y''+y'+y=(sin(x))^2 [/itex] and try to use
    [itex] y=Ae^{ix} [/itex] but then when I square it I get [itex] A^2 e^{2ix} [/itex]
    I found y' and y'' and solved for A and it didn't work I guess I could use the formula for reducing powers but I would like to try and get around that.
     
  2. jcsd
  3. Mar 26, 2014 #2

    lurflurf

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    Homework Helper

    hint
    $$(D^3+4D)(\sin(x))^2=0$$
    or
    (sin(x))^2 is a solution of y'''+4y

    chose the particular solution from those solutions
     
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