ODE
\[ 4 x^6 y''(x)+\left (1-2 x^2\right ) y(x)+4 \left (2 x^2+1\right ) x^3 y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.20677 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {e^{\frac {1}{4 x^2}} (c_2 x+c_1)}{x}\right \}\right \}\]
Maple ✓
cpu = 0.078 (sec), leaf count = 24
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {1}{4 x^{2}}}+\frac {\textit {\_C2} \,{\mathrm e}^{\frac {1}{4 x^{2}}}}{x}\right ]\] Mathematica raw input
DSolve[(1 - 2*x^2)*y[x] + 4*x^3*(1 + 2*x^2)*y'[x] + 4*x^6*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(1/(4*x^2))*(C[1] + x*C[2]))/x}}
Maple raw input
dsolve(4*x^6*diff(diff(y(x),x),x)+4*x^3*(2*x^2+1)*diff(y(x),x)+(-2*x^2+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(1/4/x^2)+_C2/x*exp(1/4/x^2)]