Differential Equations initial value problem

  • #1

Homework Statement



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

Homework Equations





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!
 

Answers and Replies

  • #2
1,481
4
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?
 
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  • #3
HallsofIvy
Science Advisor
Homework Helper
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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]
 
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