ODE
\[ (a+x) y'(x)=y(x) (1-a y(x)) \] ODE Classification
[_separable]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.32722 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {a+x}{a^2+a x+e^{c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 15
\[\left [y \left (x \right ) = \frac {a +x}{a x +\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[(a + x)*y'[x] == y[x]*(1 - a*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (a + x)/(a^2 + E^C[1] + a*x)}}
Maple raw input
dsolve((a+x)*diff(y(x),x) = y(x)*(1-a*y(x)), y(x))
Maple raw output
[y(x) = (a+x)/(a*x+_C1)]