Can anyone check my work? 1st Order ODE Initial Value Problem (Repost)

[MustangGt94]

Repost with attachment ><

1. Homework Statement

dy/dt + ty/(1+t^2) = t/(1+t^2)^1/2 y(1) = 2

Need to solve this initial value problem. The equation is a 1st order ODE

2. Homework Equations



3. The Attempt at a Solution

I've attached my solution to the problem. Just wondering if anyone can check my work. I solved the problem using the Integrating factor method u(t).

Thank You!

 

[Nolgosphere]

Your attachment is still pending approval as I write this.

Another approach is to multiply both sides by (1+t^2)^1/2 and observe that the LHS is the derivative, with respect to t, of a product. The integration becomes straight forward.