78.5.10 problem 2 (j)

Internal problem ID [18082]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 2 (j)
Date solved : Monday, March 31, 2025 at 05:07:25 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

ode:=y(x)^2+x*y(x)+1+(x^2+x*y(x)+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 5.421 (sec). Leaf size: 56

ode=( y[x]^2+x*y[x]+1 )+( x^2+x*y[x]+1 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

Timed Out