36.3.13 problem 14

Internal problem ID [6334]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 14
Date solved : Sunday, March 30, 2025 at 10:51:57 AM
CAS classification : [_separable]

\begin{align*} \frac {t y^{\prime }}{y}+1+\ln \left (y\right )&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 18

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

\[ y = {\mathrm e}^{\frac {-t c_1 +1}{t c_1}} \]

✓ Mathematica. Time used: 0.262 (sec). Leaf size: 24

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

\begin{align*} y(t)\to e^{-1+\frac {e^{c_1}}{t}} \\ y(t)\to \frac {1}{e} \\ \end{align*}

✓ Sympy. Time used: 0.430 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = e^{\frac {C_{1}}{t} - 1} \]