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`]]
\[ \boxed {\left (-y+y^{\prime } x \right ) \left (\ln \left (y\right )-\ln \left (x \right )\right )=x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve((diff(y(x),x)*x-y(x))*(ln(y(x))-ln(x))=x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \ln \left (\frac {x}{c_{1}}\right )}{\operatorname {LambertW}\left (\ln \left (\frac {x}{c_{1}}\right ) {\mathrm e}^{-1}\right )} \]
✓ Solution by Mathematica
Time used: 60.147 (sec). Leaf size: 24
DSolve[(y'[x]*x-y[x])*(Log[y[x]]-Log[x])==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x (\log (x)+c_1)}{W\left (\frac {\log (x)+c_1}{e}\right )} \]