ODE
\[ x y''(x)+y'(x)-((x+1) y(x))=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.173176 (sec), leaf count = 19
\[\left \{\left \{y(x)\to e^x (c_2 \text {Ei}(-2 x)+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.071 (sec), leaf count = 18
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{x} \expIntegral \left (1, 2 x \right )]\] Mathematica raw input
DSolve[-((1 + x)*y[x]) + y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(C[1] + C[2]*ExpIntegralEi[-2*x])}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)-(x+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(x)+_C2*exp(x)*Ei(1,2*x)]