2.1 problem 1

Internal problem ID [2580]

Book: Differential equations with applications and historial notes, George F. Simmons, 1971
Section: Chapter 2, section 8, page 41
Problem number: 1.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, [_Abel, 2nd type, class B]]

Solve \begin {gather*} \boxed {\left (x +\frac {2}{y}\right ) y^{\prime }+y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 19

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

\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (\frac {x \,{\mathrm e}^{\frac {c_{1}}{2}}}{2}\right )+\frac {c_{1}}{2}} \]

Solution by Mathematica

Time used: 60.115 (sec). Leaf size: 53

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

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