ODE
\[ (1-x) x y''(x)-2 (1-2 x) y'(x)-6 y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.030462 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {1}{3} c_2 \left (3 x^2-3 x+1\right )-c_1 (x-1)^3\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{3}+{\it \_C2}\, \left ( 3\,{x}^{2}-3\,x+1 \right ) \right \} \] Mathematica raw input
DSolve[-6*y[x] - 2*(1 - 2*x)*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((-1 + x)^3*C[1]) + ((1 - 3*x + 3*x^2)*C[2])/3}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-2*(1-2*x)*diff(y(x),x)-6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*x^3+_C2*(3*x^2-3*x+1)