Internal problem ID [1013]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 36(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y y^{\prime } x -x^{2}+y x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(x*y(x)*diff(y(x),x)=x^2-x*y(x)+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (\frac {{\mathrm e}^{-c_{1}} {\mathrm e}^{-1}}{x}\right )-c_{1}-1}+x \]
✓ Solution by Mathematica
Time used: 28.215 (sec). Leaf size: 25
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+\text {ProductLog}\left (\frac {e^{-1+c_1}}{x}\right )\right ) \\ y(x)\to x \\ \end{align*}