60.2.291 problem 869

Internal problem ID [10865]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 869
Date solved : Friday, March 14, 2025 at 02:45:27 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

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

\[ y = x^{2}+\frac {\operatorname {LambertW}\left (-2 c_{1} {\mathrm e}^{x^{4}+\frac {4}{3} x^{3}-2 x^{2}+4 x -1}\right )}{2}+\frac {1}{2} \]

✓ Mathematica. Time used: 1.018 (sec). Leaf size: 53

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

\begin{align*} y(x)\to x^2+\frac {1}{2} \left (1+W\left (-e^{x^4+\frac {4 x^3}{3}-2 x^2+4 x-1+c_1}\right )\right ) \\ y(x)\to x^2+\frac {1}{2} \\ \end{align*}

✗ Sympy

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

Timed Out