ODE
\[ \text {Y1}(y(x)) y'(x)^{n-1}+y'(x)^n=0 \] ODE Classification
[_quadrature]
Book solution method
Form \((y')^m + f_1(x,y) (y')^{m-1} \dots + f_m(x,y)=0\)
Mathematica ✓
cpu = 0.0690159 (sec), leaf count = 39
\[\left \{\left \{y(x)\to c_1+0^{\frac {1}{n}} x\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{\text {Y1}(K[1])} \, dK[1]\& \right ]\left [c_1-x\right ]\right \}\right \}\]
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