ODE
\[ x^2 (a+b x) y''(x)-2 x (2 a+b x) y'(x)+2 y(x) (3 a+b x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0362029 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {x^2 \left (c_2 x+c_1\right )}{a+b x}\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2} \left ( {\it \_C2}\,x+{\it \_C1} \right ) }{bx+a}} \right \} \] Mathematica raw input
DSolve[2*(3*a + b*x)*y[x] - 2*x*(2*a + b*x)*y'[x] + x^2*(a + b*x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^2*(C[1] + x*C[2]))/(a + b*x)}}
Maple raw input
dsolve(x^2*(b*x+a)*diff(diff(y(x),x),x)-2*x*(b*x+2*a)*diff(y(x),x)+2*(b*x+3*a)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^2*(_C2*x+_C1)/(b*x+a)