Existence, Uniqueness of a 1st Order Linear ODE

[royblaze]

Homework Statement

Solve the Cauchy problem:

(t² + 1)y' + e^tsin(t) y = sin(t) t²
y(0) = 0

Homework Equations

y'(t,y) + p(t)y = g(t,y)

Integrating factor e^{(integral of p(t))}

The Attempt at a Solution

I tried finding an integrating factor, but it came out ugly. I couldn't solve the integral.

e^{(integral of) (et * sin(t)) / (t2 + 1)}

Then I tried separating, and it didn't work out too nice either. I was considering using those psi things (as in, an exact equation approach) to find an answer, but the homework topics do not involve those. Instead, the topics are Existence and Uniqueness, Autonomous Eqns, Modeling with 1st Order ODEs.

So how do I even start this question??

 

[royblaze]

Upon reading my notes, perhaps we have not yet covered the strategy required to attack this problem? Any help is appreciated regardless.

 

[LCKurtz]

I don't think you will find any standard method to solve that. Most DE's aren't exactly solvable by elementary functions and that looks like a good candidate.