PROBLEM 5E

(a) Use the energy integral lemma to derive the family of solutions to the equation

(b) For c 0 show that these solutions are pairwise linearly independent for different values of c in an appropriate interval around t = 0.

(c) Show that none of these solutions satisfies the initial conditions y (0) =1, y’(0)= 2.

Solution

Step 1

In this problem, we have to derive the family of solution to the equation .

b) We have to show that pairwise solution is linearly independent.

c) We have to check the initial conditions whether it satisfies by the solution or not.