## Integrating Factors

If the differential equation

F(x,y) dx + G(x,y) dy = 0

is not exact, it is
possible to convert it to an exact different equation by multiplication
of an integrating factor.

By definition, if the above differential equation is not exact, it follows that F

If (F

If (F

Example:

By definition, if the above differential equation is not exact, it follows that F

_{y}≠ G_{x}, and consequently, F_{y}− G_{x}≠ 0, in addition to G_{x}− F_{y}≠ 0If (F

_{y}− G_{x})/G defined as h(x) is a function of x only, integrating factor denoted by M(x):If (F

_{y}− G_{x})/F defined as k(y) is a function of y only, integrating factor denoted by M(y):Example:

Find the integrating factor for the differential equation y dx - x dy = 0

Solution: