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Homework Help: Solving a differential equation with intial conditions, please help

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Here is the original thing:

    (x[itex]^{2}[/itex]+1)y'+4x(y-1)=0, y(0)=4

    2. Relevant equations

    3. The attempt at a solution

    I thought I knew the procedure.. but I got it wrong. Can someone let me know where I went wrong?

    First I rearrange the equation to get the following in the form y'+p(x)y=g(x)


    So I get the integrating factor to be


    That integral comes out to be 2ln(x[itex]^{2}[/itex]+1), which when raised to e, the integrating factor simply becomes


    So the new differential equation is:

    d/dx (x[itex]^{2}[/itex]+1)[itex]^{2}[/itex]y=[itex]\frac{4x}{x^{2}+1}[/itex]

    integrating both sides gets me


    solving for y:


    Taking the intial conditions into account I get C=4. When I input this equation into my assignment online, it says I'm wrong.

    Please help, I thought I knew this process pretty well..
  2. jcsd
  3. Feb 14, 2012 #2


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    You forgot to multiply the righthand side by the integrating factor.
  4. Feb 14, 2012 #3


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    Science Advisor

    So you are going to multiply both sides of the equation by that?

    Did you not multiply the right side by [itex](x^2+ 1)^2[/itex]?

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