ODE
\[ (1-x) x y'(x)+(2 x+1) y(x)=a \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.174584 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {a-3 c_1 (x-1)^3}{3 x}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 29
\[\left [y \left (x \right ) = \frac {\left (x^{3}-3 x^{2}+3 x -1\right ) \textit {\_C1}}{x}+\frac {a}{3 x}\right ]\] 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))
Maple raw output
[y(x) = (x^3-3*x^2+3*x-1)/x*_C1+1/3*a/x]