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Differential Equations initial value problem

  1. Sep 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Let f(t) be the solution to the initial value problem 2t(dy/dt)+y=t^4
    with f(0) = 0
    find f(t).

    2. Relevant equations

    3. The attempt at a solution

    I tried to do this by separating variables but that hasn't gotten me very far. I don't know if I can do it by doing that thing where you find an integrating factor and like raising e^(some integral)? It didn't really make any sense to me when I tried it, so could someone explain it please? Thanks!
  2. jcsd
  3. Sep 30, 2010 #2
    Or a cleaver substitution? Something of the form [tex]t^\alpha y[/tex] with some handy value of [tex]\alpha[/tex]? Does not the left hand side of your equation look like a derivative of a something?
    Last edited: Sep 30, 2010
  4. Sep 30, 2010 #3


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    Because it is a linear equation, there is a formula for the "integrating factor". Write it as [itex]dy/dx+ y/2t= (1/2)t^3[/itex].

    Now look for u(t) such that [itex]d(uy)/dt= u (dy/dt)+ (du/dt)y= u dy/dt+ (u/2t)y[/itex]
    Last edited by a moderator: Sep 30, 2010
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