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 = 0.171083 (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 = 0.063 (sec), leaf count = 21
\[[y \left (x \right ) = {\mathrm e}^{2 x^{2}} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{-x^{2}}]\] 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))
Maple raw output
[y(x) = exp(2*x^2)*_C1+_C2*exp(-x^2)]