ODE
\[ 4 x^3 y'(x)+x^2 y''(x)+\left (4 x^4+2 x^2+1\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.194415 (sec), leaf count = 60
\[\left \{\left \{y(x)\to \frac {1}{3} e^{-x^2} x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} \left (3 c_1-i \sqrt {3} c_2 x^{i \sqrt {3}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.118 (sec), leaf count = 41
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{\frac {1}{2}+\frac {i \sqrt {3}}{2}} {\mathrm e}^{-x^{2}}+\textit {\_C2} \,x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} {\mathrm e}^{-x^{2}}\right ]\] Mathematica raw input
DSolve[(1 + 2*x^2 + 4*x^4)*y[x] + 4*x^3*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^(1/2 - (I/2)*Sqrt[3])*(3*C[1] - I*Sqrt[3]*x^(I*Sqrt[3])*C[2]))/(3*E^x^2)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)+(4*x^4+2*x^2+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(1/2+1/2*I*3^(1/2))*exp(-x^2)+_C2*x^(1/2-1/2*I*3^(1/2))*exp(-x^2)]