ODE
\[ y''(x)-x y'(x)+2 y(x)=0 \] ODE Classification
[_Hermite]
Book solution method
TO DO
Mathematica ✓
cpu = 0.269208 (sec), leaf count = 54
\[\left \{\left \{y(x)\to \frac {1}{4} c_2 \left (\sqrt {2 \pi } \left (x^2-1\right ) \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-2 e^{\frac {x^2}{2}} x\right )+c_1 \left (x^2-1\right )\right \}\right \}\]
Maple ✓
cpu = 1.013 (sec), leaf count = 45
\[\left [y \left (x \right ) = \textit {\_C1} \left (2 x \,{\mathrm e}^{\frac {x^{2}}{2}}-\sqrt {\pi }\, \erfi \left (\frac {\sqrt {2}\, x}{2}\right ) \sqrt {2}\, \left (x -1\right ) \left (x +1\right )\right )+\textit {\_C2} \left (x^{2}-1\right )\right ]\] Mathematica raw input
DSolve[2*y[x] - x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + x^2)*C[1] + (C[2]*(-2*E^(x^2/2)*x + Sqrt[2*Pi]*(-1 + x^2)*Erfi[x/Sqrt[2]]))/4}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-x*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(2*x*exp(1/2*x^2)-Pi^(1/2)*erfi(1/2*2^(1/2)*x)*2^(1/2)*(x-1)*(x+1))+_C2*(x^2-1)]