8.5.5 problem 5

Internal problem ID [733]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 5
Date solved : Monday, January 27, 2025 at 03:00:01 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 4.040 (sec). Leaf size: 25

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

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