ODE
\[ (1-x) x y'(x)+(2 x+1) y(x)=a \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.00982764 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {a-3 c_1 (x-1)^3}{3 x}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\frac {3\, \left ( -1+x \right ) ^{3}{\it \_C1}+a}{3\,x}} \right \} \] Mathematica raw input
DSolve[(1 + 2*x)*y[x] + (1 - x)*x*y'[x] == a,y[x],x]
Mathematica raw output
{{y[x] -> (a - 3*(-1 + x)^3*C[1])/(3*x)}}
Maple raw input
dsolve(x*(1-x)*diff(y(x),x)+(1+2*x)*y(x) = a, y(x),'implicit')
Maple raw output
y(x) = 1/3*(3*(-1+x)^3*_C1+a)/x