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.