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 = 0.452045 (sec), leaf count = 62
\[\text {Solve}\left [\left \{x=\frac {\frac {a m K[1]^m}{m-1}+\frac {n K[1]^n}{n-1}}{b K[1]}+c_1,y(x)=\frac {a K[1]^m+K[1]^n}{b}\right \},\{y(x),K[1]\}\right ]\]
Maple ✓
cpu = 0.462 (sec), leaf count = 37
\[\left [y \left (x \right ) = 0, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (-\textit {\_Z}^{n}-\textit {\_Z}^{m} a +b \textit {\_a} \right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[a*y'[x]^m + y'[x]^n == b*y[x],y[x],x]
Mathematica raw output
Solve[{x == C[1] + ((a*m*K[1]^m)/(-1 + m) + (n*K[1]^n)/(-1 + n))/(b*K[1]), y[x] == (a*K[1]^m + K[1]^n)/b}, {y[x], K[1]}]
Maple raw input
dsolve(diff(y(x),x)^n+a*diff(y(x),x)^m = b*y(x), y(x))
Maple raw output
[y(x) = 0, x-Intat(1/RootOf(-_Z^n-_Z^m*a+b*_a),_a = y(x))-_C1 = 0]