Question is to find a general solution, using reduction of order to:
(1-x^2)y" - 2xy' +2y = 0
(Legendre's differential equation for n=1)
Information is given that the Legendre polynomials for the relevant n are solutions, and for n=1 this means 'x' is a solution.
The Attempt at a Solution
'x' is one solution, I need another to form the general solution. I tried solving the characteristic equation in terms of x, as shown at this link. http://www.bravus.com/Legendre.jpg [Broken]
I've included all the information from the question, any guidance in the right direction would be very welcome.
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