ODE
\[ y''(x)+2 x y'(x)-8 y(x)=0 \] ODE Classification
[_erf]
Book solution method
TO DO
Mathematica ✓
cpu = 0.150341 (sec), leaf count = 36
\[\left \{\left \{y(x)\to c_1 e^{-x^2} H_{-5}(x)+c_2 \left (\frac {4 x^4}{3}+4 x^2+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.665 (sec), leaf count = 55
\[\left [y \left (x \right ) = \textit {\_C1} \left (\left (4 x^{3}+10 x \right ) {\mathrm e}^{-x^{2}}+4 \erf \left (x \right ) \left (x^{4}+3 x^{2}+\frac {3}{4}\right ) \sqrt {\pi }\right )+\textit {\_C2} \left (4 x^{4}+12 x^{2}+3\right )\right ]\] Mathematica raw input
DSolve[-8*y[x] + 2*x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + 4*x^2 + (4*x^4)/3)*C[2] + (C[1]*HermiteH[-5, x])/E^x^2}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*x*diff(y(x),x)-8*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*((4*x^3+10*x)*exp(-x^2)+4*erf(x)*(x^4+3*x^2+3/4)*Pi^(1/2))+_C2*(4*x^4+12*x^2+3)]