Let y1 and y2 be two solutions of the equation y\'\'+P(t)y\'+Q(t)y=0 where P and

Question

Let y1 and y2 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 y1(0) = 0 =y2(0) but y1'(0) x y2'(0) does not equal 0. A. Reason that y1 and y2 do not form a fundamental set of solutions. 5. Let V1 and D2 be two solutions of the equation y" +p(th/+4@p = 0 where p and q are both continuous on R. Suppose that yi (0)0=p2(0) but y(0),s(0)0. (a) Reason that yi and yn do not form a fundamental set of solutions. (b, bonus) In fact, vi and v2 have a quantitative relation between them. Discern, state, and prove this relation.

Explanation / Answer

since y1'(0).y2'(0) not equal to 0 they do not form a fundamental solutions

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