ODE
\[ y''(x)-x y'(x)+2 y(x)=0 \] ODE Classification
[_Hermite]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0431732 (sec), leaf count = 55
\[\left \{\left \{y(x)\to c_1 \left (x^2-1\right )-\frac {1}{4} c_2 \left (2 e^{\frac {x^2}{2}} x-\sqrt {2 \pi } \left (x^2-1\right ) \text {erfi}\left (\frac {x}{\sqrt {2}}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.571 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) =2\,{{\rm e}^{1/2\,{x}^{2}}}{\it \_C1}\,x- \left ( -1+x \right ) \left ( 1+x \right ) \left ( \sqrt {2}{\it erfi} \left ( {\frac {\sqrt {2}x}{2}} \right ) \sqrt {\pi }{\it \_C1}-{\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = 2*exp(1/2*x^2)*_C1*x-(-1+x)*(1+x)*(2^(1/2)*erfi(1/2*2^(1/2)*x)*Pi^(1/2)*_C1-_C2)