8.5.6 problem 6

Internal problem ID [734]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 6
Date solved : Monday, January 27, 2025 at 03:00:07 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

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

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

\[ y = \frac {x}{2 \operatorname {LambertW}\left (\frac {x \,{\mathrm e}^{\frac {c_1}{2}}}{2}\right )} \]

✓ Solution by Mathematica

Time used: 4.395 (sec). Leaf size: 31

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

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