Let y1 and y2 be two solutions of the equation y pty qty

Let y_1 and y_2 be two solutions of the equation y\" + p(t)y\' + q(t)y = 0 where p and q are both continuous on R. Suppose that y_1(0) = 0 = y^2(0) but y\'_1(0) middot y\'_2(0) notequalto 0. Reason that y_1 and y_2 do not form a fundamental set of solutions. (b, bonus) In fact, y_1 and y_2 have a quantitative relation between them. Discern, state, and prove this relation.

Solution

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