60.2.161 problem 737

Internal problem ID [10735]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 737
Date solved : Sunday, March 30, 2025 at 06:30:56 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 28

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

\[ y = x^{2}+\frac {\operatorname {LambertW}\left (-2 c_1 \,{\mathrm e}^{\frac {4}{3} x^{3}-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]

✓ Mathematica. Time used: 0.952 (sec). Leaf size: 47

ode=D[y[x],x] == (x*(-1 + x + 2*x^3 - 2*x*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^{\frac {4 x^3}{3}-2 x^2-1+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(-x*(2*x**3 - 2*x*y(x) + x - 1)/(x**2 - y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out