47.2.29 problem 29

Internal problem ID [7445]
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
Date solved : Monday, January 27, 2025 at 02:59:56 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {y}{x +y} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 3.761 (sec). Leaf size: 25

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

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