ODE
\[ y'(x)^n=f(x) (y(x)-a)^{n+1} \] ODE Classification
[_separable]
Book solution method
Binomial equation \((y')^m + F(x) G(y)=0\)
Mathematica ✓
cpu = 0.280526 (sec), leaf count = 42
\[\left \{\left \{y(x)\to a-\left (\frac {\int _1^x(-1)^{1+\frac {1}{n}} f(K[1])^{\frac {1}{n}}dK[1]+c_1}{n}\right ){}^{-n}\right \}\right \}\]
Maple ✓
cpu = 0.692 (sec), leaf count = 26
\[\left [y \left (x \right ) = \left (\frac {n}{-\textit {\_C1} -\left (\int f \left (x \right )^{\frac {1}{n}}d x \right )}\right )^{n}+a\right ]\] Mathematica raw input
DSolve[y'[x]^n == f[x]*(-a + y[x])^(1 + n),y[x],x]
Mathematica raw output
{{y[x] -> a - ((C[1] + Inactive[Integrate][(-1)^(1 + n^(-1))*f[K[1]]^n^(-1), {K[1], 1, x}])/n)^(-n)}}
Maple raw input
dsolve(diff(y(x),x)^n = f(x)*(y(x)-a)^(n+1), y(x))
Maple raw output
[y(x) = (n/(-_C1-Int(f(x)^(1/n),x)))^n+a]