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 = 0.225095 (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 = 0.049 (sec), leaf count = 37
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \left (7 x^{2}-9 x +3\right )}{x}+\frac {\textit {\_C2} \left (6 x^{3}-6 x^{2}+1\right )}{x^{2}}\right ]\] 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))
Maple raw output
[y(x) = _C1/x*(7*x^2-9*x+3)+_C2/x^2*(6*x^3-6*x^2+1)]