second order ode help

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can you help in it ?For the solution..please write every single step. i need to understand fully

2nd order ODE

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Solve using Euler-Cauchy method:

Question 1

How to get y’ (t)
?
I don’t understand
How to get value of r?

Question 2

How it become like this?

Is this equation comply with Euler – Cauchy? Why shouldn’t
be
?Question 3:

Don’t understand the whole solution

Question 4:

Don’t understand the whole solution

Solution (cont.)

Question 5

Don’t understand the whole solution

Question 6

Don’t understand the whole solution