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 = 0.174674 (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 = 0.063 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {\left (4 x -3\right ) \textit {\_C1}}{\left (x -1\right )^{2}}+\frac {x^{4} \textit {\_C2}}{\left (x -1\right )^{2}}\right ]\] 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))
Maple raw output
[y(x) = (4*x-3)/(x-1)^2*_C1+x^4/(x-1)^2*_C2]