54.2.123 problem 699

Internal problem ID [11997]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 699
Date solved : Sunday, October 12, 2025 at 02:08:54 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 x +3} \end{align*}

✓ Maple. Time used: 0.230 (sec). Leaf size: 36

ode:=diff(y(x),x) = 1/3*x*(-2*x-2+3*x^2*(x^2+3*y(x))^(1/2))/(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ c_{1} +\frac {x^{3}}{2}-\frac {3 x^{2}}{4}+\frac {3 x}{2}-\frac {3 \ln \left (x +1\right )}{2}-\sqrt {x^{2}+3 y} = 0 \]

✓ Mathematica. Time used: 0.546 (sec). Leaf size: 47

ode=D[y[x],x] == (x*(-2 - 2*x + 3*x^2*Sqrt[x^2 + 3*y[x]]))/(3*(1 + x)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} \left (-x^2+\frac {1}{16} \left (2 x^3-3 x^2+6 x+6 \log \left (\frac {1}{x+1}\right )-6 c_1\right ){}^2\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(3*x**2*sqrt(x**2 + 3*y(x)) - 2*x - 2)/(3*x + 3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out