The differential equation y−4y^7=(y^6+6x)y′
can be written in differential form:
M(x, y)dx+N(x, y)dy=0
where
M(x, y)=
, and N(x, y)=
.

The term M(x, y)dx+N(x, y)dy becomes an exact differential if the left hand side above is divided by y^7. Integrating that new equation, the solution of the differential equation is
=C.