60.1.540 problem 553

Internal problem ID [10554]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 553
Date solved : Wednesday, March 05, 2025 at 12:04:06 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.108 (sec). Leaf size: 36

ode:=a*diff(y(x),x)^m+b*diff(y(x),x)^n-y(x) = 0; 
dsolve(ode,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*}

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

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
m = symbols("m") 
n = symbols("n") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), x)**m + b*Derivative(y(x), x)**n - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0**m, _X0**n] 
No algorithms are implemented to solve equation _X0**m*a + _X0**n*b - y(x)