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 = 0.166064 (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 = 0.069 (sec), leaf count = 26
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {1}{x}} \textit {\_C1} +\textit {\_C2} \left (x -\expIntegral \left (1, \frac {1}{x}\right ) {\mathrm e}^{\frac {1}{x}}\right )\right ]\] 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))
Maple raw output
[y(x) = exp(1/x)*_C1+_C2*(x-Ei(1,1/x)*exp(1/x))]