74.5.36 problem 38 (b)

Internal problem ID [15929]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 38 (b)
Date solved : Monday, March 31, 2025 at 02:13:39 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(t),t)-y(t)/t = ln(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (\frac {\ln \left (t \right )^{2}}{2}+c_1 \right ) t \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 19

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

\[ y(t)\to \frac {1}{2} t \left (\log ^2(t)+2 c_1\right ) \]

✓ Sympy. Time used: 0.163 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \frac {t \left (C_{1} + \log {\left (t \right )}^{2}\right )}{2} \]