There are six Rules to solve the non exact
differential equations (D.E.s) so we must learn and keep
them and choosethe proper Rule to find theIntegrating
Factor [ µ(x,y)] of the D.E. . so we must multiply I.F. by
the equation to make it an exactand then integrate it ,
but sometimes this takes long time , more paper and
more mistakes .There are two types of the first order
differential equations either an exact or non exact and
the exact D.E. can solved ( integrated )directly but for
non exact we must find the integrating factor µ(x,y). The
exact D.E. usually is the dirivative of a function of one
or many functions each one of them is linear and
iindependent on the others.
But if one function or more are rational or
logarthmic so the D.E. becomes non exact.
For me I discovred new methods to find the
integrating factor in one prcedure to solve many types of
the differential equations of the first orderin short time
with simple ways (may be without integration ) and this
will increase the FLEXIBILITY tochoose the simple
and short procedure.
There are two types of the non exact differential
equations can not solved by my method :
The homogeneous D.E. which contents the same term
in M & N togerther .
The editing D.E. which we can not find the right
integrating factor of it from M and N .
Keywords : By checking most of the D.E.s so you may write at least one of its functions directly without integration then from that function you can calculate the integrating