# Math Help - Exact? Differential equation

1. ## Exact? Differential equation

solve and Test for exactness... if not use another method
$(1-xy)^{-2}dx + (y^2+x^2(1-xy)^{-2})dy = 0$

this is not exact ... but i dont know what other method to use
need suggestion

2. The following differential equation

$M(x,y)+N(x,y)\frac{dy}{dx}=0,$

is exact iff $\frac{{\partial N}}
{{\partial x}} = \frac{{\partial M}}
{{\partial y}}.$

Did you check if this one is exact or not? Otherwise, there're 4 methods to transform an inexact ODE into a exact one.

3. yep The equation is exact when i simplify....

i need help on something else

its on solving the differential equation
since
$\frac{\partial{F}}{\partial{y}} = y^2 + x^2(1-xy)^{-2}$

$\frac{\partial{F}}{\partial{x}} = (1-xy)^{-2}$

now im integrating the dx component since it is the easiest to integrate:
$\int \frac{\partial{F}}{\partial{x}} = \int {(1-xy)}^{-2} = \frac{1}{(y(1-xy))} + Q(y)$ - since y is a constant

^
now the previous part is differentated w/ respect to y and equate with $\frac{\partial{F}}{\partial{y}}$:

so
$\frac{x}{y(1-xy)^2} - \frac{1}{y^2(1-xy)} + Q'(y) = y^2 + x^2(1-xy)^{-2}$
^
this part is my problem... i need to make it into a function of a y variable but i cannot do it correctly