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 = 0.0127617 (sec), leaf count = 16
\[\left \{\left \{y(x)\to x^2 \left (c_2 x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 13
\[ \left \{ y \left ( x \right ) ={x}^{2} \left ( {\it \_C1}\,x+{\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x^2*(_C1*x+_C2)