ODE
\[ (1-x) x y'(x)-3 x y(x)+y(x)+2=0 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.178857 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {x^2-2 x+c_1}{(x-1)^2 x}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {x^{2}+\textit {\_C1} -2 x}{x \left (x -1\right )^{2}}\right ]\] Mathematica raw input
DSolve[2 + y[x] - 3*x*y[x] + (1 - x)*x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-2*x + x^2 + C[1])/((-1 + x)^2*x)}}
Maple raw input
dsolve(x*(1-x)*diff(y(x),x)+2-3*x*y(x)+y(x) = 0, y(x))
Maple raw output
[y(x) = (x^2+_C1-2*x)/x/(x-1)^2]