Question

What is the integrating factor of the differential equation (12y+7x)dx + (-6x -4(x^2)(y^(-1))) = 0

Answer 1

\[(12y + 7x)dx + (-6x - 4x ^{2}y ^{-1})dy = 0\]

Answer 2

I think it will be helpful if you distribute first the dx's and dy's so you can isolate them later.

Answer 3

you mean multiply dx and dy by each term in the bracket?

Answer 4

Yeah.

Answer 5

\[
\mu=\exp\left(\int \frac{\frac{\partial }{\partial y}(12y+7x)-\frac{\partial }{\partial x}(−6x−4x^2y^{−1})}{−6x−4x^2y^{−1}}dx\right)
\]

Answer 6

Ooops. Sorry.

Answer 7

the real issue im having is that after ive taken the partial derivative of the first bracket with respect to y and the second bracket with respect to x: