ODE
\[ f(x) g(x)+y'(x)^n=0 \] ODE Classification
[_quadrature]
Book solution method
Form \((y')^m + X(x,y)=0\)
Mathematica ✓
cpu = 0.219884 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \int _1^x(-f(K[1]) g(K[1]))^{\frac {1}{n}}dK[1]+c_1\right \}\right \}\]
Maple ✓
cpu = 0.11 (sec), leaf count = 18
\[\left [y \left (x \right ) = \int \left (-f \left (x \right ) g \left (x \right )\right )^{\frac {1}{n}}d x +\textit {\_C1}\right ]\] Mathematica raw input
DSolve[f[x]*g[x] + y'[x]^n == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + Inactive[Integrate][(-(f[K[1]]*g[K[1]]))^n^(-1), {K[1], 1, x}]}}
Maple raw input
dsolve(diff(y(x),x)^n+f(x)*g(x) = 0, y(x))
Maple raw output
[y(x) = Int((-f(x)*g(x))^(1/n),x)+_C1]