ODE
\[ 4 x^3 y'(x)+4 x^2 y''(x)+\left (x^4+2 x^2+1\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0222109 (sec), leaf count = 28
\[\left \{\left \{y(x)\to e^{-\frac {x^2}{4}} \sqrt {x} \left (c_2 \log (x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.071 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) =\sqrt {x}{{\rm e}^{-{\frac {{x}^{2}}{4}}}} \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(1 + 2*x^2 + x^4)*y[x] + 4*x^3*y'[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[x]*(C[1] + C[2]*Log[x]))/E^(x^2/4)}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)+(x^4+2*x^2+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^(1/2)*exp(-1/4*x^2)*(ln(x)*_C2+_C1)