50.6.9 problem 1(i)

Internal problem ID [7901]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page 32
Problem number : 1(i)
Date solved : Monday, January 27, 2025 at 03:31:39 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y \ln \left (y\right )-2 y x +\left (x +y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 36

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

\[ y = {\mathrm e}^{\frac {x^{2}-x \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {x^{2}-c_{1}}{x}}}{x}\right )-c_{1}}{x}} \]

✓ Solution by Mathematica

Time used: 1.190 (sec). Leaf size: 22

DSolve[(y[x]*Log[y[x]]-2*x*y[x])+(x+y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x W\left (\frac {e^{x+\frac {c_1}{x}}}{x}\right ) \]