- #1
MidnightR
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Legendre's eq of order n>=0 is
(1-x^2)y'' -2xy' +n(n+1)y = 0.
You are given the soln y = P_n(x) for n=0,1,2,3 to be P_0(x)=1 ; P_1(x)=x ; P_2(x)=(3x^2-1)/2 ; P_3(x)=(5x^3 -3x)/2. Use reduction of order to find the second independent soln's Q_n(x)
OK I've found Q_1(x) = ln(1-x)(1+x)
I'm struggling with Q_2(x), the integrals get really horrible
Is there a faster way of doing this? Am I suppose to solve all four in this way or is there a way to do it for the general case (any n)?
Cheers
(1-x^2)y'' -2xy' +n(n+1)y = 0.
You are given the soln y = P_n(x) for n=0,1,2,3 to be P_0(x)=1 ; P_1(x)=x ; P_2(x)=(3x^2-1)/2 ; P_3(x)=(5x^3 -3x)/2. Use reduction of order to find the second independent soln's Q_n(x)
OK I've found Q_1(x) = ln(1-x)(1+x)
I'm struggling with Q_2(x), the integrals get really horrible
Is there a faster way of doing this? Am I suppose to solve all four in this way or is there a way to do it for the general case (any n)?
Cheers