60.1.550 problem 553

Internal problem ID [10564]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 553
Date solved : Monday, January 27, 2025 at 09:05:42 PM
CAS classification : [_quadrature]

\begin{align*} a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.108 (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 &= 0 \\ x -\int _{}^{y}\frac {1}{\operatorname {RootOf}\left (a \,\textit {\_Z}^{m}+b \,\textit {\_Z}^{n}-\textit {\_a} \right )}d \textit {\_a} -c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.329 (sec). Leaf size: 56

DSolve[-y[x] + a*D[y[x],x]^m + b*D[y[x],x]^n==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=\frac {a m K[1]^{m-1}}{m-1}+\frac {b n K[1]^{n-1}}{n-1}+c_1,y(x)=a K[1]^m+b K[1]^n\right \},\{y(x),K[1]\}\right ] \]