78.4.1 problem 1

Internal problem ID [18124]
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 8 (Exact Equations). Problems at page 72
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 11:29:22 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

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

dsolve((x+2/y(x))*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 6.843 (sec). Leaf size: 58

DSolve[(x+2/y[x])*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 W\left (-\frac {1}{2} \sqrt {e^{c_1} x^2}\right )}{x} \\ y(x)\to \frac {2 W\left (\frac {1}{2} \sqrt {e^{c_1} x^2}\right )}{x} \\ y(x)\to 0 \\ \end{align*}