Question

Integration factors for ODE help here. Question on the next post.

Answer 1

I have this DE: \[ (3x^2 + 2xy + y^3)dx + (x^2 + y^2)dy = 0 \]
I know that I should take the derivative of the first term (3x^2 + 2xy + y^3) with respect to y, right? And the other with respect to x.
Then we are left with: \( 3x^2 + 2x + 3y^2 \) and \( 2x\). If there is a integrating factor for this, I would pick mu(x), and I have: \[ \mu(x) ( 3x^2 + 2x + 3y^2 ) = \mu \prime(x) (2x)\]right? But I my integrating factor does not match with the answer.

Answer 2

Typo 3x^2y on the first term.

Answer 3

I got it. I forgot to do the product rule for the RHS.