Internal problem ID [6234]
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`]]
\[ \boxed {y^{2}+x y+\left (x^{2}+x y+1\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {-x^{2}+\operatorname {LambertW}\left (-2 x c_{1} {\mathrm e}^{\left (x -1\right ) \left (x +1\right )}\right )}{x} \]
✓ Solution by Mathematica
Time used: 6.606 (sec). Leaf size: 56
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 {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*}