Internal problem ID [13453]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x y y^{\prime }-y x -y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 22
dsolve(x*y(x)*diff(y(x),x)=x^2+x*y(x)+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = x \left (-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1} -1}}{x}\right )-1\right ) \]
✓ Solution by Mathematica
Time used: 4.224 (sec). Leaf size: 31
DSolve[x*y[x]*y'[x]==x^2+x*y[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \left (1+W\left (-\frac {e^{-1-c_1}}{x}\right )\right ) \\ y(x)\to -x \\ \end{align*}