4.23.23 $\text{X0}(x,y(x))y^{\prime }(x{)}^n+\text{X1}(x,y(x))y^{\prime }(x{)}^{n-1}=0$

ODE
$$\text{X0}(x,y(x))y^{\prime }(x{)}^n+\text{X1}(x,y(x))y^{\prime }(x{)}^{n-1}=0$$ ODE Classification

[_quadrature]

Book solution method
Form $X_0(x,y)(y^{\prime }{)}^m+X_1(x,y)(y^{\prime }{)}^{m-1}+\cdots +X_m(x,y)=0$

Mathematica ✗
cpu = 0.312848 (sec), leaf count = 0 , could not solve

DSolve[X1[x, y[x]]*Derivative[1][y][x]^(-1 + n) + X0[x, y[x]]*Derivative[1][y][x]^n == 0, y[x], x]

Maple ✓
cpu = 0.08 (sec), leaf count = 5

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\}$$ Mathematica raw input

DSolve[X1[x, y[x]]*y'[x]^(-1 + n) + X0[x, y[x]]*y'[x]^n == 0,y[x],x]

Mathematica raw output

DSolve[X1[x, y[x]]*Derivative[1][y][x]^(-1 + n) + X0[x, y[x]]*Derivative[1][y][x
]^n == 0, y[x], x]

Maple raw input

dsolve(X0(x,y(x))*diff(y(x),x)^n+X1(x,y(x))*diff(y(x),x)^(n-1) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1