Internal problem ID [14375]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 14
dsolve(t*(ln(t)-ln(y(t)) )*diff(y(t),t)=y(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {LambertW}\left ({\mathrm e}^{-1} c_{1} t \right )}{c_{1}} \]
✓ Solution by Mathematica
Time used: 5.377 (sec). Leaf size: 37
DSolve[t*(Log[t]-Log[y[t]] )*y'[t]==y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -e^{c_1} W\left (-e^{-1-c_1} t\right ) \\ y(t)\to 0 \\ y(t)\to \frac {t}{e} \\ \end{align*}