ODE
\[ x \left (3 x^2+1\right ) y''(x)+2 y'(x)-6 x y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.181754 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 x^2+\frac {c_1}{x}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.053 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\textit {\_C2} \left (x^{2}+1\right )\right ]\] Mathematica raw input
DSolve[-6*x*y[x] + 2*y'[x] + x*(1 + 3*x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/x + C[2] + x^2*C[2]}}
Maple raw input
dsolve(x*(3*x^2+1)*diff(diff(y(x),x),x)+2*diff(y(x),x)-6*x*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/x*_C1+_C2*(x^2+1)]