78.8.2 problem 2

Internal problem ID [18200]
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. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 11:38:00 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 1.931 (sec). Leaf size: 25

DSolve[(1-x*y[x])*D[y[x],x]==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {W\left (-e^{-c_1} x\right )}{x} \\ y(x)\to 0 \\ \end{align*}