Get the differential
equation.
Test whether the
equation
M(x,y)dx + N(x,y)dy
homogenous or not.
If f(x,y)=0, we can test it
by f(kx,ky)=k^n(x,y).
If M(x,y) and N(x,y) are
both homogenous
(degree n are the same)
If not homogenous
(degree n are different)
The ratio M/N or N/M can
be expressed of a single
variable, say v.
State non homogenous and
don't need to solve for the
general solution.
Then the substitution of
x=vy or y=vx
transforming to a variable
separable D.E.
We can use if M is
simpler, x=vy
We can use if M is
simpler, y=vx
Proceed to
substitution
Transform the
equation to a variable
separable equation
by means of separation of variable.
If
then the general solution will be