2.1309   ODE No. 1309

\[ x^3 y''(x)-\left (x^2-1\right ) y'(x)+x y(x)=0 \] Mathematica : cpu = 0.0609706 (sec), leaf count = 84

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

\[\left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {1}{2 x^2}|\begin {array}{c} 1 \\ -\frac {1}{2},-\frac {1}{2} \\\end {array}\right )+\sqrt {2} c_1 e^{\frac {1}{4 x^2}} x \left (\left (1-\frac {1}{2 x^2}\right ) \operatorname {BesselI}\left (0,\frac {1}{4 x^2}\right )+\frac {\operatorname {BesselI}\left (1,\frac {1}{4 x^2}\right )}{2 x^2}\right )\right \}\right \}\] Maple : cpu = 0.109 (sec), leaf count = 65

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

\[y \left (x \right ) = \frac {{\mathrm e}^{\frac {1}{4 x^{2}}} \left (c_{1} \left (2 x^{2}-1\right ) \operatorname {BesselI}\left (0, \frac {1}{4 x^{2}}\right )+\left (2 x^{2}-1\right ) c_{2} \operatorname {BesselK}\left (0, -\frac {1}{4 x^{2}}\right )+\operatorname {BesselI}\left (1, \frac {1}{4 x^{2}}\right ) c_{1}+\operatorname {BesselK}\left (1, -\frac {1}{4 x^{2}}\right ) c_{2}\right )}{x}\]