Prove this Theorem and Corollary

1. Use this theorem to prove the corollary given below.

**Theorem**: There are two nonzero solutions y1 and y2 to the differential equation

y''+ p(t)y' + q(t) = 0

such that one of the two functions is not a constant multiple of the other, and

that c2y1+c2y2for arbitrary constants c1 and c2 is a general solution to the

differential equation.

Corollary: If z1 and z2 are two nonzero solutions to the differential equation such that one of the two functions is not a constant multiple of the other, then c1z1 + c2z2 for arbitrary constants c1 and c2 is a general solution the

differential equation.

3. Prove the theorem stated in #2.