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 = 0.0308723 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {12 c_1 (x-1)^4+c_2 (4 x-1)}{12 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 4\,x-1 \right ) {\it \_C1}}{{x}^{2}}}+{\frac {{\it \_C2}\, \left ( -1+x \right ) ^{4}}{{x}^{2}}} \right \} \] 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*(-1 + x)^4*C[1] + (-1 + 4*x)*C[2])/(12*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) = (4*x-1)/x^2*_C1+_C2*(-1+x)^4/x^2