ODE
\[ y''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0301907 (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 = 0.078 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {{x}^{2}}{2}}}}\sqrt {\pi }\sqrt {2}{\it \_C2}+x \left ( \pi \,{\it \_C2}\,{\it Erf} \left ( {\frac {\sqrt {2}x}{2}} \right ) +{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(-1/2*x^2)*Pi^(1/2)*2^(1/2)*_C2+x*(Pi*_C2*erf(1/2*2^(1/2)*x)+_C1)