90.1.18 problem 29

Internal problem ID [25042]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 29
Date solved : Thursday, October 02, 2025 at 11:47:46 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {t +1}{t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = t +\ln \left (t \right )+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 11

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

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

✓ Sympy. Time used: 0.129 (sec). Leaf size: 8

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

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