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General solution to the differential equation

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the general solution to the differential equation:

    (d2y/dx2) - 2(dy/dx) + y = 0


    2. Relevant equations



    3. The attempt at a solution

    Is my solution correct?

    (dy/dx) - 2 + (y^2)/2 + C1 = 0

    y - 2y + (y^3)/6 + C1 + C2 = 0

    -y + (y^3)/6 + C1 + C2 = 0

    y = (y^3)/6 + C1 + C2

    Thank you
     
  2. jcsd
  3. Jan 15, 2012 #2

    rock.freak667

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    Homework Helper

    You have a 2nd order ODE with constant coefficients. You need to firstly solve the auxiliary equation formed when you substitute the trial solution y = erx.
     
  4. Jan 15, 2012 #3

    epenguin

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    Homework Helper
    Gold Member

    I think you ought to be able to recognise that as

    [tex] (\frac{d}{dx} -1)^2 y =0 [/tex]
     
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