4.31.45 ay(x)+(1x2)y(x)3xy(x)=0

ODE
ay(x)+(1x2)y(x)3xy(x)=0 ODE Classification

[_Gegenbauer]

Book solution method
TO DO

Mathematica
cpu = 0.0152825 (sec), leaf count = 58

{{y(x)c1P1a1212(x)+c2Q1a1212(x)x214}}

Maple
cpu = 0.105 (sec), leaf count = 53

{y(x)=1(_C2(x+x21)1a+_C1(x+x21)1a)1x21} Mathematica raw input

DSolve[-(a*y[x]) - 3*x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1]*LegendreP[-1/2 + Sqrt[1 - a], 1/2, x] + C[2]*LegendreQ[-1/2 + Sq
rt[1 - a], 1/2, x])/(-1 + x^2)^(1/4)}}

Maple raw input

dsolve((-x^2+1)*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-a*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C2*(x+(x^2-1)^(1/2))^(-(1-a)^(1/2))+_C1*(x+(x^2-1)^(1/2))^((1-a)^(1/2))
)/(x^2-1)^(1/2)