(a) Let y ,(t) and y2(t) be solutions of (3) on the interval a < t < /3, with y ,(to) =

Chapter 2, Problem 9

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QUESTION:

(a) Let y ,(t) and y2(t) be solutions of (3) on the interval a < t < /3, with y ,(to) = 1, y;(to) = 0, yz(to) = 0, and yi(to) = 1. Show that y,(t) and y2(t) form a fundamental set of solutions of (3) on the interval a < t < P. (b) Show that y (t) = yo y ,(t) + y&y2(t) is the solution of (3) satisfying y (to) = yo and y'(tJ = yh.

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QUESTION:

(a) Let y ,(t) and y2(t) be solutions of (3) on the interval a < t < /3, with y ,(to) = 1, y;(to) = 0, yz(to) = 0, and yi(to) = 1. Show that y,(t) and y2(t) form a fundamental set of solutions of (3) on the interval a < t < P. (b) Show that y (t) = yo y ,(t) + y&y2(t) is the solution of (3) satisfying y (to) = yo and y'(tJ = yh.

ANSWER:

Step 1 of 5

Given equation (3):

 
Given initial conditions:

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