78.1.12 problem 1 (m)

Internal problem ID [18067]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (m)
Date solved : Tuesday, January 28, 2025 at 11:24:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.133 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 2.018 (sec). Leaf size: 25

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

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