4.3.37 \(y'(x)=a f(y(x))\)

ODE
\[ y'(x)=a f(y(x)) \] ODE Classification

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

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

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

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

\[ \left \{ x-\int ^{y \relax (x ) }\!{\frac {1}{af \left ({\it \_a} \right ) }}{d{\it \_a}}+{\it \_C1}=0 \right \} \] 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