2.1192   ODE No. 1192

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

✓ Mathematica : cpu = 0.0571979 (sec), leaf count = 40

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

\[\left \{\left \{y(x)\to c_2 e^{-x} \int _1^xe^{K[1]-\frac {1}{K[1]}}dK[1]+c_1 e^{-x}\right \}\right \}\]

✓ Maple : cpu = 0.224 (sec), leaf count = 51

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

\[y \left (x \right ) = \sqrt {x}\, \left ({\mathrm e}^{-\frac {1}{x}} \operatorname {HeunD}\left (-4, 3, -8, 5, \frac {x -1}{1+x}\right ) c_{2} +\operatorname {HeunD}\left (4, 3, -8, 5, \frac {x -1}{1+x}\right ) {\mathrm e}^{-x} c_{1} \right )\]