4.5.37 $(a+x)y^{\prime }(x)=y(x)(1-ay(x))$

ODE
$$(a+x)y^{\prime }(x)=y(x)(1-ay(x))$$ ODE Classification

[_separable]

Book solution method
The Bernoulli ODE

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

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

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

$$\{{\left(y\left(x\right)\right)}^{-1}+\frac{-ax-\mathit{\_}\mathit{C}\mathit{1}}{a+x}=0\}$$ 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