ODE
\[ \left (4 x^2+1\right ) y'(x)+4 x \left (x^2+1\right ) y(x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0150125 (sec), leaf count = 21
\[\left \{\left \{y(x)\to e^{-x^2} \left (c_2 \log (x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.056 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{x}^{2}}} \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[4*x*(1 + x^2)*y[x] + (1 + 4*x^2)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + C[2]*Log[x])/E^x^2}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(4*x^2+1)*diff(y(x),x)+4*x*(x^2+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(-x^2)*(ln(x)*_C2+_C1)