60.2.197 problem 773

Internal problem ID [10771]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 773
Date solved : Sunday, March 30, 2025 at 06:36:17 PM
CAS classification : [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.221 (sec). Leaf size: 58

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

\[ y = \frac {x \left (\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (\frac {x^{2} \sec \left (\textit {\_Z} \right )^{2}}{\left (x -1\right )^{2}}\right )-\sqrt {3}\, \ln \left (3\right )+2 \sqrt {3}\, \ln \left (2\right )+2 \sqrt {3}\, c_1 -2 \textit {\_Z} \right )\right )-1\right )}{2} \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 52

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

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

✗ Sympy

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

Timed Out