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?

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- Sep 5th 2007, 12:22 PMObstacle12nd order differential equation
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? - Sep 5th 2007, 01:15 PMtopsquark
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 - Sep 5th 2007, 06:19 PMThePerfectHacker
- Sep 6th 2007, 04:35 AMObstacle1