Internal problem ID [3120]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (y x -x^{2}\right ) y^{\prime }-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve((x*y(x)-x^2)*diff(y(x),x)=y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = -x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1}}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 2.286 (sec). Leaf size: 25
DSolve[(x*y[x]-x^2)*y'[x]==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x W\left (-\frac {e^{-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}