4.3.37 $y^{\prime }(x)=af(y(x))$

ODE
$$y^{\prime }(x)=af(y(x))$$ ODE Classification

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

Mathematica ✓
cpu = 0.0654202 (sec), leaf count = 25

$$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{f(K[1])}dK[1]\mathrm{\&}][ax+c_1]\}\right\}$$

Maple ✓
cpu = 0.008 (sec), leaf count = 21

$$\{x-{\int }^{y\left(x\right)}\frac{1}{af\left(\mathit{\_}\mathit{a}\right)}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[y'[x] == a*f[y[x]],y[x],x]

Mathematica raw output

{{y[x] -> InverseFunction[Integrate[f[K[1]]^(-1), {K[1], 1, #1}] & ][a*x + C[1]]
}}

Maple raw input

dsolve(diff(y(x),x) = a*f(y(x)), y(x),'implicit')

Maple raw output

x-Intat(1/a/f(_a),_a = y(x))+_C1 = 0