ODE No. 1208

\[ x^3 y'(x)+x^2 y''(x)+\left (x^2-2\right ) y(x)=0 \] Mathematica : cpu = 0.043866 (sec), leaf count = 59

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

\[\left \{\left \{y(x)\to \frac {c_2 e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } e^{\frac {x^2}{2}} \text {erf}\left (\frac {x}{\sqrt {2}}\right )-2 x\right )}{2 x}+\frac {c_1}{x}\right \}\right \}\] Maple : cpu = 0.048 (sec), leaf count = 35

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

\[y \left (x \right ) = \frac {\sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, x}{2}\right ) c_{2}-2 \,{\mathrm e}^{-\frac {x^{2}}{2}} c_{2} x +c_{1}}{x}\]