ODE
\[ x^3 y''(x)+x y'(x)-2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0143923 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{x}} \text {Ei}\left (-\frac {1}{x}\right )+c_1 x+c_2 e^{\frac {1}{x}}\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) =-{{\rm e}^{{x}^{-1}}}{\it Ei} \left ( 1,{x}^{-1} \right ) {\it \_C2}+{{\rm e}^{{x}^{-1}}}{\it \_C1}+{\it \_C2}\,x \right \} \] Mathematica raw input
DSolve[-2*y[x] + x*y'[x] + x^3*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + E^x^(-1)*C[2] + E^x^(-1)*C[1]*ExpIntegralEi[-x^(-1)]}}
Maple raw input
dsolve(x^3*diff(diff(y(x),x),x)+x*diff(y(x),x)-2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = -exp(1/x)*Ei(1,1/x)*_C2+exp(1/x)*_C1+_C2*x