ODE
\[ y'(x)=f(x) g(y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.200586 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{g(K[1])}dK[1]\& \right ]\left [\int _1^xf(K[2])dK[2]+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 20
\[\left [\int f \left (x \right )d x -\left (\int _{}^{y \left (x \right )}\frac {1}{g \left (\textit {\_a} \right )}d \textit {\_a} \right )+\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x] == f[x]*g[y[x]],y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][g[K[1]]^(-1), {K[1], 1, #1}] & ][C[1] + Inactive[Integrate][f[K[2]], {K[2], 1, x}]]}}
Maple raw input
dsolve(diff(y(x),x) = f(x)*g(y(x)), y(x))
Maple raw output
[Int(f(x),x)-Intat(1/g(_a),_a = y(x))+_C1 = 0]