Internal problem ID [6182]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
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`]]
\[ \boxed {\left (x +\frac {2}{y}\right ) y^{\prime }+y=0} \]
✓ 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)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (\frac {x \,{\mathrm e}^{\frac {c_{1}}{2}}}{2}\right )+\frac {c_{1}}{2}} \]
✓ Solution by Mathematica
Time used: 17.046 (sec). Leaf size: 58
DSolve[(x+2/y[x])*y'[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*}