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?
Well, if you happen to stumble over a solution reduction of order will work well. Here's a general method.
Note that the order of the coefficient of is n. Thus this is an Euler differential equation.
So, make a change of variables:
And
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 .
-Dan