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Solve differential equation

  1. Mar 30, 2012 #1

    sharks

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    Gold Member

    The problem statement, all variables and given/known data
    Solve [tex]\frac{dy(t)}{dt}+2ty(t)=5t
    \\y(0)=1[/tex]

    The attempt at a solution
    Since this is a 1st order ODE, i find the integrating factor,
    [tex]μ(t)=e^{\int P(t).dt}
    \\P(t)=2t
    \\Q(t)=5t
    \\μ(t)=e^{t^2}
    [/tex]
    Using formula:
    [tex]\frac{dμy}{dt}=μQ[/tex]
    Integrating both R.H.S. and L.H.S.:
    [tex]μy=\int e^{t^2}.5t\,.dt
    \\μy=\frac{5}{2}e^{t^2}+A
    \\y=\frac{5}{2}+\frac{A}{e^{t^2}}
    [/tex]
    Using y(0)=1
    When t=0, y=1
    [itex]1=\frac{5}{2}+A[/itex], so A=1-(5/2)=-3/2

    Therefore, the particular solution is: y=(5/2)-(3/2) which gives y=1.

    Is this answer correct?
     
    Last edited: Mar 30, 2012
  2. jcsd
  3. Mar 30, 2012 #2

    jgens

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    Gold Member

    It looks correct to me.
     
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