The differential equation of type exact differential equation when





Examples :



1.



2.



3. The differential equation (where M and N are function of x and y) is called anwhen ( where u is a function of x and y). is an exact differential equation as is an exact differential equation as The differential equation



Necessary and sufficient condition

Article. Find the necessary and sufficient condition that the equation



Proof 1. Necessary condition





2. Condition is sufficient



is an exact differential equations as Find the necessary and sufficient condition that the equation ( where M and N are function of x and y with the condition that are continuous function of x and y) may be exact.Necessary conditionCondition is sufficient

Integrating factor

Five rules for finding integrating factor

An integrating factor (abbreviatef I.F) of a differential equation is such a factor such that if the equation is multiplied by it, the result equation is exact.If is not exact and it is difficult to find integrating factor, then following five rules help us in finding integrating factor.If the equation is homogenous in x and y i.e. if M and N are homogenous function of the same degree in x and y, then is an I.F. provided If the equation is of the form , then is an I.F. provided If the equation is a function of x only =f(x) then is an I.F.If the equation is a function of y only =f(y) then is an I.F.If the equation is