A Level Maths Notes: FP1 – Transforming and Solving Non - Linear, Non – Homogeneous Differential Equations
Non linear differential equations contain one of more products
of
or
terms or maybe powers of these terms or even products of powers. They
may look more complicated but they can often be transformed into a
simpler form and solved using the one of standard techniques of
separation of variables, the integrating factor method or the
procedure for solving linear equations.
Example:
(1).
Use the transformation
and
find the general solution of the resulting equation.
Substitute these into (1)
.
This last equation has complementary solution
and
particular solution
hence
so
and
