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 = 0.037903 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 x^2+\frac {c_1}{x}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {x}^{3}+x \right ) {\it \_C2}+{\it \_C1}}{x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = ((x^3+x)*_C2+_C1)/x