ODE
\[ f(x) g(x)+y'(x)^n=0 \] ODE Classification
[_quadrature]
Book solution method
Form \((y')^m + X(x,y)=0\)
Mathematica ✓
cpu = 0.110586 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \int _1^x (-f(K[1]) g(K[1]))^{\frac {1}{n}} \, dK[1]+c_1\right \}\right \}\]
Maple ✓
cpu = 0.051 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) =\int \!\sqrt [n]{-f \left ( x \right ) g \left ( x \right ) }\,{\rm d}x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[f[x]*g[x] + y'[x]^n == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1] + 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),'implicit')
Maple raw output
y(x) = Int((-f(x)*g(x))^(1/n),x)+_C1