(a) Prove that the set of solutions to the homogeneous ordinary differential equation u - 4u +...

Question:

(a) Prove that the set of solutions to the homogeneous ordinary differential equation uʹʹ - 4uʹ + 3 u = 0 forms a vector space.
(b) Write the solution space as the span of a finite number of functions.
(c) What is the minimal number of functions needed to span the solution space?