60.2.22 problem 598

Internal problem ID [10596]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 598
Date solved : Sunday, March 30, 2025 at 06:09:22 PM
CAS classification : [[_homogeneous, `class D`]]

\begin{align*} y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right )}{x -1} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(y(x),x) = (y(x)+F(y(x)/x))/(x-1); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} -\ln \left (x \right )+\ln \left (x -1\right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 45

ode=D[y[x],x] == (F[y[x]/x] + y[x])/(-1 + x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{F(K[1])+K[1]}dK[1]=\int _1^x\frac {1}{(K[2]-1) K[2]}dK[2]+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
F = Function("F") 
ode = Eq(Derivative(y(x), x) - (F(y(x)/x) + y(x))/(x - 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (F(y(x)/x) + y(x))/(x - 1) cannot be solved by the lie group method