47.2.14 problem 14

Internal problem ID [7430]
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 : 14
Date solved : Monday, January 27, 2025 at 02:56:23 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

dsolve(x*diff(y(x),x)-y(x)=y(x)*diff(y(x),x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 4.072 (sec). Leaf size: 27

DSolve[x*D[y[x],x]-y[x]==y[x]*D[y[x],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*}