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IVP and Uniqueness problem

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve the IVP and determine if the solution is unique and explain why.

    2. Relevant equations

    t*y'+(t-2)y=t^4*e^t, y(0)=0

    3. The attempt at a solution

    t*y'+(t-2)y=t^4*e^t

    y'+ ((t-2)/t)y=t^3*e^t

    integration factor=e^(integral((t-2)/t dt)=e^t/(t^2)

    d/dy((e^t/t^2)*y=t*e^(2t)

    integrate both sides

    (e^t/t^2)*y=e^(2t)*(t/2-1/4)+C

    y=((t^3)/2-(t^2)/4)*e^t+(t^2*C)/e^t

    y(0)=0----> 0=(0/2-0/4)*e^0+(0*C)/e^0, so how would i find the value for C and can someone explain the concept of uniqueness? I couldnt really follow my russian professor :-p
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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