# Math Help - Verify that ... is an integrating factor?

1. ## Verify that ... is an integrating factor?

By differentiating the equation:
$\int \frac{f(xy) + F(xy)}{f(xy) - F(xy)}\cdot \frac{d(xy)}{xy} + \ln \left(\frac{x}{y}\right) = c$
verify that:
$\frac{1}{xy\{f(xy) - F(xy)\}}$
is an integrating factor of $f(xy)\ y\ dx + F(xy)\ x\ dy = 0$

2. Call the intergrating factor P. Differentiate the given equation to verify
$

\frac{\partial }{\partial y}(P(x,y)f(xy)y)=\frac{\partial }{\partial x}(P(x,y)F(xy)x).

$