(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

See above.

3. 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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# Legendre differential equation and reduction of order

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