54.2.257 problem 834

Internal problem ID [12131]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 834
Date solved : Sunday, October 12, 2025 at 02:22:15 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x \left (x +1\right )} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 68

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

\[ \frac {x y^{2}}{6 y^{2}+x} = \frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (x^{2} {\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {x \left ({\mathrm e}^{\textit {\_Z}}+9\right )}{\left (x +1\right )^{2}}\right )+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 c_1 \,{\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-2 x \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9\right ) x}{54} \]

✓ Mathematica. Time used: 0.316 (sec). Leaf size: 86

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

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

✗ Sympy

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

Timed Out