4.23.20 $\text{Y1}(y(x))y^{\prime }(x{)}^{n-1}+y^{\prime }(x{)}^n=0$

ODE
$$\text{Y1}(y(x))y^{\prime }(x{)}^{n-1}+y^{\prime }(x{)}^n=0$$ ODE Classification

[_quadrature]

Book solution method
Form $(y^{\prime }{)}^m+f_1(x,y)(y^{\prime }{)}^{m-1}\cdots +f_m(x,y)=0$

Mathematica ✓
cpu = 0.0690159 (sec), leaf count = 39

$$\{\{y(x)\to c_1+0^{\frac{1}{n}}x\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{\text{Y1}(K[1])}dK[1]\mathrm{\&}][c_1-x]\}\}$$

Maple ✗
cpu = 0.052 (sec), leaf count = 0 , exception

numeric exception: division by zero

Mathematica raw input

DSolve[Y1[y[x]]*y'[x]^(-1 + n) + y'[x]^n == 0,y[x],x]

Mathematica raw output

{{y[x] -> 0^n^(-1)*x + C[1]}, {y[x] -> InverseFunction[Integrate[Y1[K[1]]^(-1), 
{K[1], 1, #1}] & ][-x + C[1]]}}

Maple raw input

dsolve(diff(y(x),x)^n+Y1(y(x))*diff(y(x),x)^(n-1) = 0, y(x),'implicit')

Maple raw output

numeric exception: division by zero