ODE
\[ (1-2 x) (1-x) x^2 y''(x)+2 (2-3 x) x y'(x)+2 (3 x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0626712 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \frac {c_2 \left (12 x^2-18 x+7\right )-3 c_1 (x-1)^3}{3 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 7\,{\it \_C1}+6\,{\it \_C2} \right ) {x}^{3}+ \left ( -9\,{\it \_C1}-6\,{\it \_C2} \right ) {x}^{2}+3\,{\it \_C1}\,x+{\it \_C2}}{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[2*(1 + 3*x)*y[x] + 2*(2 - 3*x)*x*y'[x] + (1 - 2*x)*(1 - x)*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-3*(-1 + x)^3*C[1] + (7 - 18*x + 12*x^2)*C[2])/(3*x^2)}}
Maple raw input
dsolve(x^2*(1-x)*(1-2*x)*diff(diff(y(x),x),x)+2*x*(2-3*x)*diff(y(x),x)+2*(1+3*x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ((7*_C1+6*_C2)*x^3+(-9*_C1-6*_C2)*x^2+3*_C1*x+_C2)/x^2