solve and Test for exactness... if not use another method
$\displaystyle (1-xy)^{-2}dx + (y^2+x^2(1-xy)^{-2})dy = 0$
this is not exact ... but i dont know what other method to use
need suggestion
The following differential equation
$\displaystyle M(x,y)+N(x,y)\frac{dy}{dx}=0,$
is exact iff $\displaystyle \frac{{\partial N}}
{{\partial x}} = \frac{{\partial M}}
{{\partial y}}.$
Did you check if this one is exact or not? Otherwise, there're 4 methods to transform an inexact ODE into a exact one.
yep The equation is exact when i simplify....
i need help on something else
its on solving the differential equation
since
$\displaystyle \frac{\partial{F}}{\partial{y}} = y^2 + x^2(1-xy)^{-2}$
$\displaystyle \frac{\partial{F}}{\partial{x}} = (1-xy)^{-2}$
now im integrating the dx component since it is the easiest to integrate:
$\displaystyle \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 $\displaystyle \frac{\partial{F}}{\partial{y}}$:
so
$\displaystyle \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