Internal problem ID [14297]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact]
\[ \boxed {\ln \left (t y\right )=-\frac {t y^{\prime }}{y}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve(ln(t*y(t))+t/y(t)*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{\frac {t +c_{1}}{t}}}{t} \]
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 19
DSolve[Log[t*y[t]]+t/y[t]*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{1+\frac {c_1}{t}}}{t} \]