Internal problem ID [3852]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 3.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (y-x \right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve((y(x)-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 3.968 (sec). Leaf size: 25
DSolve[(y[x]-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{W\left (-e^{-c_1} x\right )+c_1} \\ y(x)\to 0 \\ \end{align*}