Internal problem ID [6233]
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')`]
\[ \boxed {y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x^{2}-x \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {x^{2}-c_{1}}{x}}}{x}\right )-c_{1}}{x}} \]
✓ Solution by Mathematica
Time used: 1.073 (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]
\[ y(x)\to x W\left (\frac {e^{x+\frac {c_1}{x}}}{x}\right ) \]