90.12.5 problem 5

Internal problem ID [25207]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 213
Problem number : 5
Date solved : Thursday, October 02, 2025 at 11:58:56 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \ln \left (t \right )+\frac {c_1}{t}-1 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.101 (sec). Leaf size: 10

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

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