Internal problem ID [5024]
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]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x +y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve(diff(y(x),x)=y(x)/(x+y(x)),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\LambertW \left (x \,{\mathrm e}^{c_{1}}\right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 60.026 (sec). Leaf size: 18
DSolve[y'[x]==y[x]/(x+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{\text {ProductLog}\left (e^{-c_1} x\right )} \\ \end{align*}