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Differential equation

  1. Jun 22, 2008 #1
    The problem statement, all variables and given/known data
    Verify that the general solution satisfies the differential equation. Then find the particular solution that satisfies the initial condition.

    y=C1+C2 lnx

    xy'' + y' = 0

    y=0 when x=2
    y'=(1/2) when x=2

    The attempt at a solution

    Here's what I did so far....

    y=C1+C2 lnx
    y'=C1+C2(1/x)
    y''=C1+C2(-1/x^2)

    Since xy''+y'=0 I then substituted y' and y'' into the equation.

    x(C1+C2(-1/x^2))+(C1+C2(1/x))=0

    After this step I am stuck. If you could help push me in the right direction that would be great. Also could you verify that what I already did is right?
     
  2. jcsd
  3. Jun 22, 2008 #2

    kreil

    User Avatar
    Gold Member

    The derivative of a constant is zero, as I'm sure you're aware, so C1 drops out of y' and y''

    then since [itex]y'+xy''=0[/itex] you have [tex]\frac{C2}{x}-\frac{C2x}{x^2}=\frac{C2}{x}-\frac{C2}{x}=0[/tex] as desired.

    The second part is just plugging in some numbers, [itex](2)(y'')+\frac{1}{2}=0 \implies y''= - \frac{1}{4}[/itex]
     
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