ODE
\[ (1-x) x y'(x)=a+(x+1) y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0123901 (sec), leaf count = 24
\[\left \{\left \{y(x)\to -\frac {a x \log (x)+a-c_1 x}{(x-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={\frac {-a\ln \left ( x \right ) x+{\it \_C1}\,x-a}{ \left ( -1+x \right ) ^{2}}} \right \} \] Mathematica raw input
DSolve[(1 - x)*x*y'[x] == a + (1 + x)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -((a - x*C[1] + a*x*Log[x])/(-1 + x)^2)}}
Maple raw input
dsolve(x*(1-x)*diff(y(x),x) = a+(1+x)*y(x), y(x),'implicit')
Maple raw output
y(x) = (-a*ln(x)*x+_C1*x-a)/(-1+x)^2