t^2*y'' - 2t*y' + y = 0
To get the solution do you need to do a reduction of order? If so how do you get one solution, trial and error?
Note that the order of the coefficient of is n. Thus this is an Euler differential equation.
So, make a change of variables:
So the differential equation becomes:
This is a linear homogeneous differential equation with constant coefficients and is easy to solve. So solve it and re-sub in .