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Homework Help: Ordinary differentiation equations (ODE)-seperable

  1. Mar 24, 2010 #1
    hey there..
    i've got unsolved solution here..


    Solve initial value problem..

    xy’ – y = 2x2y ; y(1) = 1



    x dy/dx = y + 2x2y

    dy/dx = y/x + 2xy

    dy/dx = y[(1/x) + 2x]

    ∫1/y dy = ∫ (1/x) + 2x dx

    ln |y| = ln |x| + x2 + C

    apply exp to both side

    y = x + ex^2 + e^C



    substitute the initial value

    1 = 1 + e1 + e^C

    e^(1+C) = 0

    apply ln

    1 + C = ln 0?
     
  2. jcsd
  3. Mar 24, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    You are forgetting your basic exponential rules:

    [tex]y=e^{\ln(x)+x^2+c}=e^ce^{x^2}e^{\ln(x)}\neq x+e^{x^2}+e^c[/tex]
     
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