31.4.4 problem 3

Internal problem ID [5743]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 5
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:12:25 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y+\left (2 y-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 17

dsolve(y(x)+(2*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x}{2 \operatorname {LambertW}\left (-\frac {x \,{\mathrm e}^{-\frac {c_{1}}{2}}}{2}\right )} \]

✓ Solution by Mathematica

Time used: 4.449 (sec). Leaf size: 33

DSolve[y[x]+(2*y[x]-x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{2 W\left (-\frac {1}{2} e^{-1-\frac {c_1}{2}} x\right )} \\ y(x)\to 0 \\ \end{align*}