50.6.10 problem 1(j)

Internal problem ID [7902]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page 32
Problem number : 1(j)
Date solved : Monday, January 27, 2025 at 03:31:39 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 5.402 (sec). Leaf size: 56

DSolve[(y[x]^2+x*y[x]+1)+(x^2+x*y[x]+1)*D[y[x],x]==0,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*}