ODE
\[ y''(x)+2 x y'(x)-8 y(x)=0 \] ODE Classification
[_erf]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00584071 (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 = 0.182 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) = \left ( 4\,{\it \_C1}\,{x}^{3}+10\,{\it \_C1}\,x \right ) {{\rm e}^{-{x}^{2}}}+4\, \left ( {x}^{4}+3\,{x}^{2}+3/4 \right ) \left ( {\it Erf} \left ( x \right ) \sqrt {\pi }{\it \_C1}+{\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = (4*_C1*x^3+10*_C1*x)*exp(-x^2)+4*(x^4+3*x^2+3/4)*(erf(x)*Pi^(1/2)*_C1+_C2)