ODE
\[ y'(x)=a f(y(x)) \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Independent variable missing
Mathematica ✓
cpu = 0.195219 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{f(K[1])}dK[1]\& \right ][a x+c_1]\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 21
\[\left [x -\left (\int _{}^{y \left (x \right )}\frac {1}{a f \left (\textit {\_a} \right )}d \textit {\_a} \right )+\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x] == a*f[y[x]],y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[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))
Maple raw output
[x-Intat(1/a/f(_a),_a = y(x))+_C1 = 0]