2.1213   ODE No. 1213

\[ \left (x^3+1\right ) x y'(x)+x^2 y''(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.0591991 (sec), leaf count = 54

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

\[\left \{\left \{y(x)\to \frac {\sqrt [3]{3} c_1 \, _1F_1\left (-\frac {1}{3};\frac {1}{3};-\frac {x^3}{3}\right )}{x}+\frac {c_2 x \, _1F_1\left (\frac {1}{3};\frac {5}{3};-\frac {x^3}{3}\right )}{\sqrt [3]{3}}\right \}\right \}\]

✓ Maple : cpu = 0.083 (sec), leaf count = 53

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

\[y \left (x \right ) = \left (c_{1} \operatorname {BesselI}\left (-\frac {1}{6}, \frac {x^{3}}{6}\right )+c_{1} \operatorname {BesselI}\left (\frac {5}{6}, \frac {x^{3}}{6}\right )-c_{2} \left (-\operatorname {BesselK}\left (\frac {5}{6}, \frac {x^{3}}{6}\right )+\operatorname {BesselK}\left (\frac {1}{6}, \frac {x^{3}}{6}\right )\right )\right ) {\mathrm e}^{-\frac {x^{3}}{6}} x^{{3}/{2}}\]