ODE
\[ x^2 y''(x)-4 x y'(x)+6 y(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163052 (sec), leaf count = 16
\[\left \{\left \{y(x)\to x^2 (c_2 x+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 15
\[[y \left (x \right ) = \textit {\_C2} \,x^{3}+x^{2} \textit {\_C1}]\] Mathematica raw input
DSolve[6*y[x] - 4*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2*(C[1] + x*C[2])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = 0, y(x))
Maple raw output
[y(x) = _C2*x^3+_C1*x^2]