2.1316   ODE No. 1316

\[ x \left (x^2-1\right ) y''(x)+\left (x^2-1\right ) y'(x)-x y(x)=0 \]

✓ Mathematica : cpu = 0.0567553 (sec), leaf count = 38

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

\[\left \{\left \{y(x)\to c_2 G_{2,2}^{2,0}\left (x^2|\begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\\end {array}\right )+\frac {2 c_1 E\left (x^2\right )}{\pi }\right \}\right \}\]

✓ Maple : cpu = 0.049 (sec), leaf count = 18

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

\[y \left (x \right ) = c_{1} \operatorname {EllipticE}\left (x \right )+c_{2} \left (\operatorname {EllipticCE}\left (x \right )-\operatorname {EllipticCK}\left (x \right )\right )\]