54.2.314 problem 893

Internal problem ID [12188]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 893
Date solved : Wednesday, October 01, 2025 at 01:08:00 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 x^{2} y^{2}+12 x y+8}{x^{3}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 41

ode:=diff(y(x),x) = (6*x+x^3+x^3*y(x)^2+4*x^2*y(x)+x^3*y(x)^3+6*x^2*y(x)^2+12*x*y(x)+8)/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {29 \operatorname {RootOf}\left (-81 \int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} +x +3 c_1 \right ) x -3 x -18}{9 x} \]

✓ Mathematica. Time used: 0.1 (sec). Leaf size: 58

ode=D[y[x],x] == (8 + 6*x + x^3 + 12*x*y[x] + 4*x^2*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^2 + x^3*y[x]^3)/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {x+6}{x}+3 y(x)}{\sqrt [3]{29}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**3*y(x)**3 + x**3*y(x)**2 + x**3 + 6*x**2*y(x)**2 + 4*x**2*y(x) + 12*x*y(x) + 6*x + 8)/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out