The function satisfies the linear equation
The Wronskian, , of two independent solutions denoted and is defined to be
Let be given. In this case, show that the expression for can be interpreted as a first-order inhomogeneous differential equation for . Hence, by explicit derivation, show that may be expressed as
where the rôle of should be briefly elucidated.
Show that satisfies
Verify that is a solution of
Hence, using with and expanding the integrand in powers of to order , find the first three non-zero terms in the power series expansion for a solution, , of ( ) that is independent of and satisfies .