ODE
\[ y''(x)+x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0189758 (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 = 0.028 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={({\it Erf} \left ( {\frac {i}{2}}\sqrt {2}x \right ) {\it \_C1}+{\it \_C2}) \left ( {{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) ^{-1}} \right \} \] 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),'implicit')
Maple raw output
y(x) = (erf(1/2*I*2^(1/2)*x)*_C1+_C2)/exp(1/2*x^2)