78.3.20 problem 6 (c)

Internal problem ID [18123]
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. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 6 (c)
Date solved : Tuesday, January 28, 2025 at 11:29:20 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 17

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

\[ y = \frac {\operatorname {LambertW}\left (x^{2} {\mathrm e}^{-2 c_1}\right )}{x} \]

✓ Solution by Mathematica

Time used: 60.421 (sec). Leaf size: 31

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

\[ y(x)\to \frac {W\left (e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )} x^2\right )}{x} \]