Internal problem ID [2650]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 14.
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 {x^{2}-y x +y^{2}-y y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve((x^2-x*y(x)+y(x)^2)-x*y(x)*diff(y(x),x)=0,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: 28.294 (sec). Leaf size: 25
DSolve[(x^2-x*y[x]+y[x]^2)-x*y[x]*y'[x]==0,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*}