Monday, 13 January 2014

Exact Equation

 

The differential equation     Mdx+Ndy=0    ,

where both    and   N   are functions of     and   y     is said to be exact when there is a function     u     of     x, y    such that 

Mdx+Ndy=du ,

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

DM/Dy=DN/Dx

The method of solving and exact equation of the type

Mdx+Ndy=0   .

First integrate the term in   Mdx   as if    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 .



No comments:

Post a Comment

Our Latest Post

Introduction of Circle

All of my lessons and teaching videos are in English and most of them are for students of Logistics Management. But many of mys students an...

Popular Post