Internal problem ID [13073]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (x +y\right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve((y(x)+x)*diff(y(x),x)=y(x),y(x), singsol=all)
\[ y = {\mathrm e}^{\operatorname {LambertW}\left ({\mathrm e}^{c_{1}} x \right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 3.407 (sec). Leaf size: 23
DSolve[(y[x]+x)*y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{W\left (e^{-c_1} x\right )} y(x)\to 0 \end{align*}