4.5.37 \((a+x) y'(x)=y(x) (1-a y(x))\)

ODE
\[ (a+x) y'(x)=y(x) (1-a y(x)) \] ODE Classification

[_separable]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0224721 (sec), leaf count = 22

\[\left \{\left \{y(x)\to \frac {a+x}{a^2+a x+e^{c_1}}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 22

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}+{\frac {-ax-{\it \_C1}}{a+x}}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)+(-a*x-_C1)/(a+x) = 0