ODE
\[ (1-x) x y'(x)=a+2 (2-x) y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.172599 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {a (4 x-3)+12 c_1 x^4}{12 (x-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 29
\[\left [y \left (x \right ) = \frac {\left (-a \left (\frac {1}{4 x^{4}}-\frac {1}{3 x^{3}}\right )+\textit {\_C1} \right ) x^{4}}{\left (x -1\right )^{2}}\right ]\] Mathematica raw input
DSolve[(1 - x)*x*y'[x] == a + 2*(2 - x)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (a*(-3 + 4*x) + 12*x^4*C[1])/(12*(-1 + x)^2)}}
Maple raw input
dsolve(x*(1-x)*diff(y(x),x) = a+2*(2-x)*y(x), y(x))
Maple raw output
[y(x) = (-a*(1/4/x^4-1/3/x^3)+_C1)*x^4/(x-1)^2]