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Homework Help: I'm stuck

  1. Jun 15, 2005 #1
    I need to solve this D.E.

    [tex]x^2y''-xy' + y = x^3[/tex]

    i'm supposed to use the variation of parameters technique.

    in that technique i need to get a coeffecient of 1 in the first postion of y'' and then sove the homogenous D.E.

    [tex]y''-\frac{y'}{x} +\frac{y}{x^2}=0[/tex]

    the above leads to

    [tex] m^2-2m +1=0[/tex]

    now solving this i get

    [tex]C_1x +C_2tx[/tex]

    my problem is that i don't know how to move forward with
    [tex]C_2tx[/tex]

    how do i proceed
     
    Last edited: Jun 15, 2005
  2. jcsd
  3. Jun 15, 2005 #2

    dextercioby

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    It's an Euler equation.You need to transform it into a linear equation with constant coeffs.Read the theory again and identify the substitution you need.

    Daniel.
     
  4. Jun 15, 2005 #3
    do you mean that this is a Bernoulli equation?
     
  5. Jun 15, 2005 #4

    dextercioby

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    I told u it was/is an Euler eqn.

    Make the sub

    [tex] x=e^{t} [/tex]

    [tex] y(x)\longrightarrow \bar{y}(t) [/tex]

    Daniel.
     
    Last edited: Jun 15, 2005
  6. Jun 15, 2005 #5
    ok. i'll figure it out
     
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