ODE
\[ -8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0174306 (sec), leaf count = 26
\[\left \{\left \{y(x)\to e^{-x^2} \left (c_1 e^{3 x^2}+c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.031 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{2\,{x}^{2}}}+{\it \_C2}\,{{\rm e}^{-{x}^{2}}} \right \} \] Mathematica raw input
DSolve[-8*x^3*y[x] - (1 + 2*x^2)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(3*x^2)*C[1] + C[2])/E^x^2}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(2*x^2+1)*diff(y(x),x)-8*x^3*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*exp(2*x^2)+_C2*exp(-x^2)