ODE
\[ 4 x^6 y''(x)+\left (8 x^4+10 x^2+1\right ) y(x)-4 \left (2 x^2+1\right ) x^3 y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0289315 (sec), leaf count = 23
\[\left \{\left \{y(x)\to e^{-\frac {1}{4 x^2}} x \left (c_2 x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.048 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) =x{{\rm e}^{-{\frac {1}{4\,{x}^{2}}}}} \left ( {\it \_C2}\,x+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(1 + 10*x^2 + 8*x^4)*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] -> (x*(C[1] + x*C[2]))/E^(1/(4*x^2))}}
Maple raw input
dsolve(4*x^6*diff(diff(y(x),x),x)-4*x^3*(2*x^2+1)*diff(y(x),x)+(8*x^4+10*x^2+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*exp(-1/4/x^2)*(_C2*x+_C1)