ODE
\[ y''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.190514 (sec), leaf count = 45
\[\left \{\left \{y(x)\to -\sqrt {\frac {\pi }{2}} c_2 x \text {erf}\left (\frac {x}{\sqrt {2}}\right )-c_2 e^{-\frac {x^2}{2}}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.168 (sec), leaf count = 35
\[\left [y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \left (-\frac {\sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, x}{2}\right ) x}{2}-{\mathrm e}^{-\frac {x^{2}}{2}}\right )\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] - C[2]/E^(x^2/2) - Sqrt[Pi/2]*x*C[2]*Erf[x/Sqrt[2]]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*(-1/2*Pi^(1/2)*2^(1/2)*erf(1/2*2^(1/2)*x)*x-exp(-1/2*x^2))]