The differential equation

*,*

**Mdx+Ndy=0**where both

*and*

**M***are functions of*

**N***and*

**x***is said to be exact when there is a function*

**y***of*

**u***such that*

**x, y**

**Mdx+Ndy=du ,**i.e. , when

*becomes a partial differential .*

**Mdx+Ndy**Now , we know from Differential Calculus that ;

*should be a perfect differential if ;*

**Mdx+Ndy***, Hence the condition that*

**DM/Dy=DN/Dx***should be an exact differential equation is*

**Mdx+Ndy=0**

**DM/Dy=DN/Dx**The method of solving and exact equation of the type

*.*

**Mdx+Ndy=0**First integrate the term in

*as if*

**Mdx***were constant then integrate the terms in*

**y***considering*

**Ndy***as constant and rejecting the terms already obtained equate the sum of these integrals to a constant .*

**x**