60.2.248 problem 824

Internal problem ID [10822]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 824
Date solved : Wednesday, March 05, 2025 at 01:05:12 PM
CAS classification : [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (x -1\right ) \left (x +y\right )} \end{align*}

✓ Maple. Time used: 1.261 (sec). Leaf size: 61

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

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

✓ Mathematica. Time used: 0.153 (sec). Leaf size: 56

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**3 + x**2*y(x) + y(x)**2)*y(x)/(x**2*(x - 1)*(x + y(x))),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out