54.2.399 problem 978

Internal problem ID [12273]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 978
Date solved : Wednesday, October 01, 2025 at 01:26:45 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Abel]

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

✓ Maple. Time used: 0.183 (sec). Leaf size: 64

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

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

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 35

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

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded