ODE
\[ (1-2 x) (1-x) y''(x)+2 (3-4 x) y'(x)+12 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0381852 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {1}{3} c_2 \left (12 x^2-18 x+7\right )-c_1 (x-1)^3\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 18\,{\it \_C1}+7\,{\it \_C2} \right ) {x}^{3}}{3}}+{\frac { \left ( -18\,{\it \_C1}-9\,{\it \_C2} \right ) {x}^{2}}{3}}+{\it \_C2}\,x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[12*y[x] + 2*(3 - 4*x)*y'[x] + (1 - 2*x)*(1 - x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((-1 + x)^3*C[1]) + ((7 - 18*x + 12*x^2)*C[2])/3}}
Maple raw input
dsolve((1-x)*(1-2*x)*diff(diff(y(x),x),x)+2*(3-4*x)*diff(y(x),x)+12*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/3*(18*_C1+7*_C2)*x^3+1/3*(-18*_C1-9*_C2)*x^2+_C2*x+_C1