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 = 0.180695 (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 = 0.055 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {\left (-1+4 x \right ) \textit {\_C1}}{x^{2}}+\frac {\textit {\_C2} \left (x -1\right )^{4}}{x^{2}}\right ]\] 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))
Maple raw output
[y(x) = (-1+4*x)/x^2*_C1+_C2/x^2*(x-1)^4]