Internal problem ID [3779]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 527.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x \left (-y+x \right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(x*(x-y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1}}}{x}\right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 2.271 (sec). Leaf size: 25
DSolve[x(x-y[x])y'[x]+y[x]^2==0,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*}