60.2.10 problem 586

Internal problem ID [10584]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 586
Date solved : Friday, March 14, 2025 at 02:13:44 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {F \left (\frac {y}{\sqrt {x^{2}+1}}\right ) x}{\sqrt {x^{2}+1}} \end{align*}

✓ Maple. Time used: 0.080 (sec). Leaf size: 64

ode:=diff(y(x),x) = F(y(x)/(x^2+1)^(1/2))*x/(x^2+1)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \operatorname {RootOf}\left (-F \left (\frac {\textit {\_Z}}{\sqrt {x^{2}+1}}\right ) \sqrt {x^{2}+1}+\textit {\_Z} \right ) \\ y &= \operatorname {RootOf}\left (-\ln \left (x^{2}+1\right )+2 \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )-\textit {\_a}}d \textit {\_a} \right )+2 c_{1} \right ) \sqrt {x^{2}+1} \\ \end{align*}

✓ Mathematica. Time used: 0.396 (sec). Leaf size: 975

ode=D[y[x],x] == (x*F[y[x]/Sqrt[1 + x^2]])/Sqrt[1 + x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
F = Function("F") 
ode = Eq(-x*F(y(x)/sqrt(x**2 + 1))/sqrt(x**2 + 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out