Internal problem ID [1006]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A]]
Solve \begin {gather*} \boxed {\left (y^{\prime } x -y\right ) \left (\ln \relax (y)-\ln \relax (x )\right )-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.04 (sec). Leaf size: 19
dsolve((diff(y(x),x)*x-y(x))*(ln(y(x))-ln(x))=x,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\LambertW \left (\left (\ln \relax (x )+c_{1}\right ) {\mathrm e}^{-1}\right )+1} x \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 21
DSolve[(y'[x]*x-y[x])*(Log[y[x]]-Log[x])==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x e^{1+\text {ProductLog}\left (\frac {\log (x)+c_1}{e}\right )} \\ \end{align*}