# Legendre's differential equation

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Legendre's differential equation, i.e. , (1-x^2)y''(x) - 2xy'(x) + n(n+1)y(x)=0. Find all solutions to Legendre's differential equation assuming solutions of the form y(x) = P r (x).

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Power series solution obtained (attached).

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:44 pm ad1c9bdddf>https://brainmass.com/math/calculus-and-analysis/finding-solutions-legendres-differential-equation-215031