88.1.7 problem 21

Internal problem ID [23950]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 6
Problem number : 21
Date solved : Thursday, October 02, 2025 at 09:46:44 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {t^{2}+1}{t \left (t -2\right )} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(t),t) = (t^2+1)/t/(t-2); 
dsolve(ode,y(t), singsol=all);
 

\[ y = t -\frac {\ln \left (t \right )}{2}+\frac {5 \ln \left (t -2\right )}{2}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

ode=D[y[t],t]==(t^2+1)/(t*(t-2)); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t+\frac {5}{2} \log (2-t)-\frac {\log (t)}{2}+c_1 \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - (t**2 + 1)/(t*(t - 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + t - \frac {\log {\left (t \right )}}{2} + \frac {5 \log {\left (t - 2 \right )}}{2} \]