2.1241   ODE No. 1241

(1v)(v+2)y(x)+(x21)y(x)2xy(x)=0

Mathematica : cpu = 0.0091675 (sec), leaf count = 30

DSolve[(1 - v)*(2 + v)*y[x] - 2*x*Derivative[1][y][x] + (-1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
 
{{y(x)c1(x21)Pv2(x)+c2(x21)Qv2(x)}}

Maple : cpu = 0.066 (sec), leaf count = 24

dsolve((x^2-1)*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-(v+2)*(v-1)*y(x)=0,y(x))
 
y(x)=(x1)(1+x)(c2LegendreQ(v,2,x)+c1LegendreP(v,2,x))