ODE
\[ y''(x)+x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.160697 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{2} e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } c_1 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+2 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.049 (sec), leaf count = 33
\[\left [y \left (x \right ) = \erf \left (\frac {i \sqrt {2}\, x}{2}\right ) {\mathrm e}^{-\frac {x^{2}}{2}} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{-\frac {x^{2}}{2}}\right ]\] Mathematica raw input
DSolve[y[x] + x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[2] + Sqrt[2*Pi]*C[1]*Erfi[x/Sqrt[2]])/(2*E^(x^2/2))}}
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) = erf(1/2*I*2^(1/2)*x)/exp(1/2*x^2)*_C1+_C2/exp(1/2*x^2)]