ODE
\[ x^2 y''(x)+2 x y'(x)-6 y(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0169455 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \frac {c_1 x^5+c_2}{x^3}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{5}{\it \_C2}+{\it \_C1}}{{x}^{3}}} \right \} \] Mathematica raw input
DSolve[-6*y[x] + 2*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^5*C[1] + C[2])/x^3}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*x^5+_C1)/x^3