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Use the method of reduction of order to find a second solution y2 of the given...

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Advance Math

Use the method of reduction of order to find a second solutiony2 of the given differential equation such that {y1, y2} is afundamental set of solutions on the given interval.

t2y?? +2ty? ?2y=0, t > 0, y1(t)=t

(a) Verify that the two solutions that you have obtained arelinearly independent.

(b) Let y(1) = y0, y?(1) = v0. Solve the initial value problem.What is the longest interval on which the initial value problem iscertain to have a unique twice differentiable solution?

(c) Now suppose that y(0) = y0, y?(0) = v0. Is there a solutionin this case (how does it depend on y0 and v0? If so, how many?Explain.

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