Question

I'm having a little trouble with this ODE. (1+x^2)y'-2xy=2x(1+x^2).
p(x) should equal to -2x/(1+x^2)
Therefor the integrating factor should be e^-ln(1+x^2)=-(1+x^2)
Then -(1+x^2)y=integral(-2x(x^2 + 1))
meaning -x^4/-2(x^2 +1) - (x^2/-(x^2 +1)) +c/(x^2 +1). WolframAlpha shows that the answer is "y(x) = c_1 (x^2+1)+(x^2+1) ln(x^2+1)". What am I doing wrong?

Answer 1

I did the same mistake too... in a beginning...
Actually, the problem is:
-ln(1+x^2)= ln (1/(1+x^2)
so your integrating factor is= 1/(1+x^2)
not: -(1+x^2)
if you use it - you get your answer...
Let me know if you need help on that :)

Answer 2

d(y/(1+x^2))=2x/(1+x^2)
y/(1+x^2) = ln(1+x^2) +C

Answer 3

did you finished it...?
equations?

Answer 4

Thank you so much. I've been killing myself over this problem for a day. I swear, I'm never going to make that mistake again!

Answer 5

I did the same mistake... honest!
when you posted the answer - start digging...
:))