54.2.331 problem 910

Internal problem ID [12205]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 910
Date solved : Wednesday, October 01, 2025 at 01:13:19 AM
CAS classification : [_rational, _Abel]

\begin{align*} y^{\prime }&=\frac {-2 x -y+1+x^{2} y^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 42

ode:=diff(y(x),x) = (-2*x-y(x)+1+x^2*y(x)^2+2*x^3*y(x)+x^4+x^3*y(x)^3+3*x^4*y(x)^2+3*x^5*y(x)+x^6)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-9 x^{2}+29 \operatorname {RootOf}\left (-81 \int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} +x +3 c_1 \right )-3}{9 x} \]

✓ Mathematica. Time used: 1.12 (sec). Leaf size: 76

ode=D[y[x],x] == (1 - 2*x + x^4 + x^6 - y[x] + 2*x^3*y[x] + 3*x^5*y[x] + x^2*y[x]^2 + 3*x^4*y[x]^2 + x^3*y[x]^3)/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {3 x^3+3 y(x) x^2+x}{\sqrt [3]{29} \sqrt [3]{x^3}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {29^{2/3} \left (x^3\right )^{2/3}}{9 x}+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**6 + 3*x**5*y(x) + 3*x**4*y(x)**2 + x**4 + x**3*y(x)**3 + 2*x**3*y(x) + x**2*y(x)**2 - 2*x - y(x) + 1)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out