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 = 0.153423 (sec), leaf count = 71
\[\left \{\left \{y(x)\to \frac {1}{2} \sqrt {\pi } c_2 \sqrt {x^2} \left (2 x^2-3\right ) \text {erfi}\left (\sqrt {x^2}\right )+8 c_1 x^3-c_2 e^{x^2} x^2+c_2 e^{x^2}-12 c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.506 (sec), leaf count = 24
\[\left [y \left (x \right ) = \textit {\_C1} \left (-\frac {2}{3} x^{3}+x \right )+\textit {\_C2} \hypergeom \left (\left [-\frac {3}{2}\right ], \left [\frac {1}{2}\right ], x^{2}\right )\right ]\] Mathematica raw input
DSolve[6*y[x] - 2*x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -12*x*C[1] + 8*x^3*C[1] + E^x^2*C[2] - E^x^2*x^2*C[2] + (Sqrt[Pi]*Sqrt[x^2]*(-3 + 2*x^2)*C[2]*Erfi[Sqrt[x^2]])/2}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*x*diff(y(x),x)+6*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(-2/3*x^3+x)+_C2*hypergeom([-3/2],[1/2],x^2)]