60.2.308 problem 886

Internal problem ID [10882]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 886
Date solved : Sunday, March 30, 2025 at 07:19:12 PM
CAS classification : [_rational, _Abel]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 42

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

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

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 60

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

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

✗ Sympy

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

Timed Out