ODE
\[ \text {X0}(x,y(x)) y'(x)^n+\text {X1}(x,y(x)) y'(x)^{n-1}=0 \] ODE Classification
[_quadrature]
Book solution method
Form \(X_0(x,y) (y')^m + X_1 (x,y) (y')^{m-1} + \dots + X_m(x,y)=0\)
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
\[ \left \{ y \left ( x \right ) ={\it \_C1} \right \} \] 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