Internal problem ID [5023]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {y}{y+x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(diff(y(x),x)=y(x)/(x+y(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {LambertW}\left (x \,{\mathrm e}^{c_{1}}\right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 3.413 (sec). Leaf size: 23
DSolve[y'[x]==y[x]/(x+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{W\left (e^{-c_1} x\right )} \\ y(x)\to 0 \\ \end{align*}