5.5 problem 5

Internal problem ID [83]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\[ \boxed {x \left (x +y\right ) y^{\prime }-y \left (x -y\right )=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 14

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

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

Solution by Mathematica

Time used: 4.218 (sec). Leaf size: 25

DSolve[x*(x+y[x])*y'[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*}