Question

This is for Differential Equations. I was sick last week and missed class so I do...

This is for Differential Equations. I was sick last week and missed class so I do not understand the process behind solving this question.

Problem 3 Consider the ODE t 2 y'' + 3 t y' + y = 0.

• Factorize the left hand side of the ODE. Hint: One of the factors is (D + 2 t -1 I).

• Find the fundamental set of solutions.

• Solve the initial value problem t 2 y'' + 3 t y' + y = 0, y (1) = 1, y' (1) = 0

Any help would be greatly appreciated, I am especially confused about the factorization part. Please show all steps and work I need to understand the process behind each problem. Thanks in advance!

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