ODE
\[ a y'(x)^m+y'(x)^n=b y(x) \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.202146 (sec), leaf count = 56
\[\text {Solve}\left [\left \{x=\frac {\frac {a m \text {K$\$$252469}^m}{m-1}+\frac {n \text {K$\$$252469}^n}{n-1}}{b \text {K$\$$252469}}+c_1,y(x)=\frac {a \text {K$\$$252469}^m+\text {K$\$$252469}^n}{b}\right \},\{y(x),\text {K$\$$252469}\}\right ]\]
Maple ✓
cpu = 0.052 (sec), leaf count = 37
\[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( -{{\it \_Z}}^{n}-{{\it \_Z}}^{m}a+b{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[a*y'[x]^m + y'[x]^n == b*y[x],y[x],x]
Mathematica raw output
Solve[{x == ((a*K$252469^m*m)/(-1 + m) + (K$252469^n*n)/(-1 + n))/(b*K$252469) + C[1], y[x] == (a*K$252469^m + K$252469^n)/b}, {y[x], K$252469}]
Maple raw input
dsolve(diff(y(x),x)^n+a*diff(y(x),x)^m = b*y(x), y(x),'implicit')
Maple raw output
y(x) = 0, x-Intat(1/RootOf(-_Z^n-_Z^m*a+b*_a),_a = y(x))-_C1 = 0