Internal problem ID [8133]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 553.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {a \left (y^{\prime }\right )^{m}+b \left (y^{\prime }\right )^{n}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 36
dsolve(a*diff(y(x),x)^m+b*diff(y(x),x)^n-y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {1}{\RootOf \left (a \,\textit {\_Z}^{m}+b \,\textit {\_Z}^{n}-\textit {\_a} \right )}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 56
DSolve[-y[x] + a*y'[x]^m + b*y'[x]^n==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {a m K[1]^{m-1}}{m-1}+\frac {b n K[1]^{n-1}}{n-1}+c_1,y(x)=a K[1]^m+b K[1]^n\right \},\{y(x),K[1]\}\right ] \]