ODE
\[ y'(x)^n=a x^r+b y'(x)^s \] ODE Classification
[_quadrature]
Book solution method
Change of variable
Mathematica ✗
cpu = 0.0213661 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x]^n == a*x^r + b*Derivative[1][y][x]^s, y[x], x]
Maple ✓
cpu = 0.063 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) =\int \!{\it RootOf} \left ( -{{\it \_Z}}^{n}+a{x}^{r}+b{{\it \_Z}}^{s} \right ) \,{\rm d}x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[y'[x]^n == a*x^r + b*y'[x]^s,y[x],x]
Mathematica raw output
DSolve[Derivative[1][y][x]^n == a*x^r + b*Derivative[1][y][x]^s, y[x], x]
Maple raw input
dsolve(diff(y(x),x)^n = a*x^r+b*diff(y(x),x)^s, y(x),'implicit')
Maple raw output
y(x) = Int(RootOf(-_Z^n+a*x^r+b*_Z^s),x)+_C1