31.1.7 problem 3.1

Internal problem ID [5705]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 3.1
Date solved : Monday, January 27, 2025 at 01:09:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y-x \right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 17

dsolve((y(x)-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 4.048 (sec). Leaf size: 27

DSolve[(y[x]-x)*D[y[x],x]+y[x]==0,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*}