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 = 0.0271307 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {e^{\frac {1}{4 x^2}} \left (c_2 x+c_1\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.049 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,x+{\it \_C2}}{x}{{\rm e}^{{\frac {1}{4\,{x}^{2}}}}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(1/4/x^2)*(_C1*x+_C2)/x