The differential equation Mdx+Ndy=0 ,
where both M and N are functions of x and y is said to be exact when there is a function u of x, y such that
i.e. , when Mdx+Ndy becomes a partial differential .
Now , we know from Differential Calculus that ;
Mdx+Ndy should be a perfect differential if ;
DM/Dy=DN/Dx , Hence the condition that
Mdx+Ndy=0 should be an exact differential equation is
The method of solving and exact equation of the type
First integrate the term in Mdx as if y were constant then integrate the terms in Ndy considering x as constant and rejecting the terms already obtained equate the sum of these integrals to a constant .