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General solution of ode

  1. Apr 19, 2010 #1
    Question: find the general solution of xX' = aX

    i know it's kinda simple ode.. but, i just dont know y i cant get the correct answer..

    solution..

    xX' = aX
    x dX/dx = aX
    d/dx X = aX/x
    X = ∫aX/x dx
    X = aX ln |x| + C

    the general solution is Ax^a

    problem : i cant get the correct answer..
     
  2. jcsd
  3. Apr 19, 2010 #2

    lanedance

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    Homework Helper

    is X a function x? if so thats prettty messy notation

    how about starting with
    [tex] xy'(x) = ay [/tex]

    then
    [tex] x\frac{dy}{dx} = ay [/tex]

    the idea when rearranging is to "separate" the DE, so group all the y's on one side & x's on the other side - if you can do that it means its a "seperable DE"
    [tex] \frac{dy}{x} = a\frac{dx}{x} [/tex]

    now try intergating both sides
     
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