60.2.289 problem 867

Internal problem ID [10863]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 867
Date solved : Sunday, March 30, 2025 at 07:17:28 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27} \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 30

ode:=diff(y(x),x) = -2/3*x+1+y(x)^2+2/3*x^2*y(x)+1/9*x^4+y(x)^3+x^2*y(x)^2+1/3*y(x)*x^4+1/27*x^6; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 55

ode=D[y[x],x] == 1 - (2*x)/3 + x^4/9 + x^6/27 + (2*x^2*y[x])/3 + (x^4*y[x])/3 + y[x]^2 + x^2*y[x]^2 + y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**6/27 - x**4*y(x)/3 - x**4/9 - x**2*y(x)**2 - 2*x**2*y(x)/3 + 2*x/3 - y(x)**3 - y(x)**2 + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out