28.1.14 problem 14

Internal problem ID [4320]
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
Date solved : Monday, January 27, 2025 at 09:02:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x^{2}-y x +y^{2}-x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 19

dsolve((x^2-x*y(x)+y(x)^2)-x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (1+\operatorname {LambertW}\left (\frac {{\mathrm e}^{-c_{1} -1}}{x}\right )\right ) \]

✓ Solution by Mathematica

Time used: 3.227 (sec). Leaf size: 25

DSolve[(x^2-x*y[x]+y[x]^2)-x*y[x]*D[y[x],x]==0,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*}