Internal problem ID [14437]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.953 (sec). Leaf size: 14
dsolve([(y(t)/t+ln(y(t)))+(t/y(t)+ln(t))*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t \operatorname {LambertW}\left (\frac {\ln \left (t \right )}{t}\right )}{\ln \left (t \right )} \]
✓ Solution by Mathematica
Time used: 1.922 (sec). Leaf size: 18
DSolve[{(y[t]/t+Log[y[t]])+(t/y[t]+Log[t])*y'[t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t W\left (\frac {\log (t)}{t}\right )}{\log (t)} \]