74.8.35 problem 35

Internal problem ID [16100]
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 : Monday, March 31, 2025 at 02:43:14 PM
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*}

✓ Maple. Time used: 0.320 (sec). Leaf size: 17

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

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

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

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

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

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t/y(t) + log(t))*Derivative(y(t), t) + log(y(t)) + y(t)/t,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out