how can you proove that (xy+1)dx+x(x+4y-2)dy=0, where you will have an answer of xy+lnx+2y^2-2y=c?

Question

differential equation solution.

Answer 1

By differentiation of

Answer 2

xy+lnx+2y^2-2y=c

Answer 3

We have:

Answer 4

xdy+ ydx+dx/x+4ydy-2dy=0

Answer 5

x^2 dy+(xy)dx+dx+(4xy-2x) dy=0

Answer 6

(xy+1)dx+x(x+4y-2) dy=0

Answer 7

Qed,

Answer 8

Note: the integrating factor

Answer 9

-if we solve the given differential equation

Answer 10

- is F= 1/x