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 = 0.293822 (sec), leaf count = 46
\[\text {Solve}\left [\left \{x=\frac {a \log (\text {K$\$$201926})+\frac {n \text {K$\$$201926}^{n-1}}{n-1}}{b}+c_1,y(x)=\frac {a \text {K$\$$201926}+\text {K$\$$201926}^n}{b}\right \},\{y(x),\text {K$\$$201926}\}\right ]\]
Maple ✓
cpu = 0.046 (sec), leaf count = 33
\[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( {{\it \_Z}}^{n}+a{\it \_Z}-b{\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[a*y'[x] + y'[x]^n == b*y[x],y[x],x]
Mathematica raw output
Solve[{x == C[1] + ((K$201926^(-1 + n)*n)/(-1 + n) + a*Log[K$201926])/b, y[x] == (a*K$201926 + K$201926^n)/b}, {y[x], K$201926}]
Maple raw input
dsolve(diff(y(x),x)^n+a*diff(y(x),x) = b*y(x), y(x),'implicit')
Maple raw output
y(x) = 0, x-Intat(1/RootOf(_Z^n+a*_Z-b*_a),_a = y(x))-_C1 = 0