Internal problem ID [5480]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y \ln \relax (y)-2 x y+\left (x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 34
dsolve((y(x)*ln(y(x))-2*x*y(x))+(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x \LambertW \left (\frac {{\mathrm e}^{x} {\mathrm e}^{-\frac {c_{1}}{x}}}{x}\right )-x^{2}+c_{1}}{x}} \]
✓ Solution by Mathematica
Time used: 1.523 (sec). Leaf size: 22
DSolve[(y[x]*Log[y[x]]-2*x*y[x])+(x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \text {ProductLog}\left (\frac {e^{x+\frac {c_1}{x}}}{x}\right ) \\ \end{align*}