I've been working on this hw problem for a while now, but I'm stuck in the integration process. I'm pretty sure I made an error, cause I can't seem to be able to integrate the right side of the equation.

Question

Q: (1/(x^(2)+1))y' + xy = 3

using the equation d/dx(ry)=f(x)r(x) I found r(x) to be e^((1/4)x^(4) + (1/2)x^(2)). Plugging it back into the equation I have d/dx(ry)=(3x^(2)+3)(e^((1/4)x^(4) + (1/2)x^(2))). I tried u-substitution to integrate, but it's not working out. Please explain how to go about this problem, I'd like to know where my mistake is. Thanks!

Answer 1

Hmmm. It appears your integrating factor is correct. Evaluating the right-hand side is intractable.

a couple of online solvers both come up with y in terms of that integral, which is not evaluated.

Beats me.

Answer 2

I see, thanks!