ODE
\[ a y'(x)+y'(x)^n=b y(x) \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.586437 (sec), leaf count = 51
\[\text {Solve}\left [\left \{x=\frac {a \log (K[1])+\frac {n K[1]^{n-1}}{n-1}}{b}+c_1,y(x)=\frac {a K[1]+K[1]^n}{b}\right \},\{y(x),K[1]\}\right ]\]
Maple ✓
cpu = 0.711 (sec), leaf count = 33
\[\left [y \left (x \right ) = 0, x -\left (\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (\textit {\_Z}^{n}+a \textit {\_Z} -b \textit {\_a} \right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[a*y'[x] + y'[x]^n == b*y[x],y[x],x]
Mathematica raw output
Solve[{x == C[1] + ((n*K[1]^(-1 + n))/(-1 + n) + a*Log[K[1]])/b, y[x] == (a*K[1] + K[1]^n)/b}, {y[x], K[1]}]
Maple raw input
dsolve(diff(y(x),x)^n+a*diff(y(x),x) = b*y(x), y(x))
Maple raw output
[y(x) = 0, x-Intat(1/RootOf(_Z^n+a*_Z-b*_a),_a = y(x))-_C1 = 0]