54.2.289 problem 868

Internal problem ID [12163]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 868
Date solved : Wednesday, October 01, 2025 at 01:03:38 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 57

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

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

✗ Sympy

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

Timed Out