Internal problem ID [5481]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve((y(x)^2+x*y(x)+1)+(x^2+x*y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-x^{2}+\LambertW \left (-2 x \,{\mathrm e}^{x^{2}} c_{1} {\mathrm e}^{-1}\right )}{x} \]
✓ Solution by Mathematica
Time used: 60.187 (sec). Leaf size: 26
DSolve[(y[x]^2+x*y[x]+1)+(x^2+x*y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\frac {\text {ProductLog}\left (x \left (-e^{x^2-1+c_1}\right )\right )}{x} \\ \end{align*}