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.
