Internal problem ID [3890]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 5
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (2 y-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(y(x)+(2*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {LambertW}\left (-\frac {x \,{\mathrm e}^{-\frac {c_{1}}{2}}}{2}\right )+\frac {c_{1}}{2}} \]
✓ Solution by Mathematica
Time used: 4.742 (sec). Leaf size: 31
DSolve[y[x]+(2*y[x]-x)*y'[x]==0,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*}