ODE
\[ y''(x)-2 x y'(x)+6 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0122955 (sec), leaf count = 85
\[\left \{\left \{y(x)\to \frac {\sqrt {\pi } c_2 \left (2 x^2-3\right ) x^2 \text {erfi}\left (\sqrt {x^2}\right )+2 \sqrt {x^2} \left (8 c_1 x^3-c_2 e^{x^2} x^2+c_2 e^{x^2}-12 c_1 x\right )}{2 \sqrt {x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.243 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{\mbox {$_1$F$_1$}(-{\frac {3}{2}};\,{\frac {1}{2}};\,{x}^{2})}+{\frac { \left ( -2\,{x}^{3}+3\,x \right ) {\it \_C1}}{3}} \right \} \] Mathematica raw input
DSolve[6*y[x] - 2*x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*Sqrt[x^2]*(-12*x*C[1] + 8*x^3*C[1] + E^x^2*C[2] - E^x^2*x^2*C[2]) + Sqrt[Pi]*x^2*(-3 + 2*x^2)*C[2]*Erfi[Sqrt[x^2]])/(2*Sqrt[x^2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*x*diff(y(x),x)+6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C2*hypergeom([-3/2],[1/2],x^2)+1/3*(-2*x^3+3*x)*_C1