Existence of Fundamental Solution Sets. By Theorem 1, for each j = 1, 2, . . . , n there is a unique solution to equation (17) satisfying the initial conditions (a) Show that {y1,y2, . . . ,yn} is a fundamental solution set for (17). [Hint: Write out the Wronskian at x0.] (b) For given initial values express the solution y(x) to (17) satisfying [as in equations (4)] in terms of this fundamental solution set.

Solution Step 1 Here it is given that And as per (17)a) The wronskian will be So => Hence is a fundamental solution set .