60.2.39 problem 615

Internal problem ID [10613]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 615
Date solved : Sunday, March 30, 2025 at 06:10:24 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 38

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

\begin{align*} y &= 0 \\ y &= \operatorname {RootOf}\left (F \left (x \textit {\_Z} \right )\right ) \\ -y+\int _{}^{x y}\frac {1}{F \left (\textit {\_a} \right ) \textit {\_a}}d \textit {\_a} -c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.222 (sec). Leaf size: 77

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

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

✗ Sympy

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

Timed Out