Unfortunately, Theorem 1 .23 does not show us how to find two independent solutions. How...

Unfortunately, Theorem 1 .23 does not show us how to find two independent solutions. However, there is a technique that can be used to find a second solution when one solution is known.

(a) Show that is a solution of

(b) Let where v is a yet to be determined function of t. Note that if is non-constant, then are independent. Show that the substitution reduces equation (1.32) to the separable equation

Solve equation (1.33) for v, form the solution , and then state the general solution of equation (1.32).

Reference: Theorem 1 .23: