74.8.35 problem 35

Internal problem ID [16171]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 08:55:49 AM
CAS classification : [_exact]

\begin{align*} \frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 2.193 (sec). Leaf size: 17

dsolve([(y(t)/t+ln(y(t)))+(t/y(t)+ln(t))*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
 

\[ y = \frac {t \operatorname {LambertW}\left (\frac {\ln \left (t \right )}{t}\right )}{\ln \left (t \right )} \]

✓ Solution by Mathematica

Time used: 60.307 (sec). Leaf size: 18

DSolve[{(y[t]/t+Log[y[t]])+(t/y[t]+Log[t])*D[y[t],t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t W\left (\frac {\log (t)}{t}\right )}{\log (t)} \]