ODE
\[ (1-x) x y''(x)-3 y'(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0271246 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {12 c_1 x^4+4 c_2 x-3 c_2}{12 (x-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{4}{\it \_C2}+4\,{\it \_C1}\,x-3\,{\it \_C1}}{ \left ( -1+x \right ) ^{2}}} \right \} \] Mathematica raw input
DSolve[2*y[x] - 3*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (12*x^4*C[1] - 3*C[2] + 4*x*C[2])/(12*(-1 + x)^2)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*x^4+4*_C1*x-3*_C1)/(-1+x)^2