(a) Verify that are linearly independent solutions of the differential equation on t...

(a) Verify that are linearly independent solutions of the differential equation on the interval (-∞,∞).

(b) Show that for every real number x. Does this result violate Theorem 3.1.3? Explain.

(c) Verify that are also linearly independent solutions of the differential equation in part (a) on the interval (-∞,∞).

(d) Find a solution of the differential equation satisfying

(e) By the superposition principle, Theorem 3.1.2, both linear combinations are solutions of the differential equation. Discuss whether one, both, or neither of the linear combinations is a general solution of the differential equation on the interval (-∞,∞).