ODE No. 1239

\[ -l y(x)+\left (x^2-1\right ) y''(x)+2 x y'(x)=0 \] Mathematica : cpu = 0.0098678 (sec), leaf count = 46

DSolve[-(l*y[x]) + 2*x*Derivative[1][y][x] + (-1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 P_{\frac {1}{2} \left (\sqrt {4 l+1}-1\right )}(x)+c_2 Q_{\frac {1}{2} \left (\sqrt {4 l+1}-1\right )}(x)\right \}\right \}\] Maple : cpu = 0.048 (sec), leaf count = 35

dsolve((x^2-1)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-l*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{1} \LegendreP \left (\frac {\sqrt {1+4 l}}{2}-\frac {1}{2}, x\right )+c_{2} \LegendreQ \left (\frac {\sqrt {1+4 l}}{2}-\frac {1}{2}, x\right )\]