74.3.24 problem 19

Internal problem ID [15805]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 19
Date solved : Thursday, March 13, 2025 at 06:44:58 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{t -3}&=\frac {1}{t -1} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Maple. Time used: 0.058 (sec). Leaf size: 26

ode:=diff(y(t),t)+1/(t-3)*y(t) = 1/(t-1); 
ic:=y(-1) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {t -2 \ln \left (t -1\right )+1+2 \ln \left (2\right )+2 i \pi }{t -3} \]

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 32

ode=D[y[t],t]+1/(t-3)*y[t]==1/(t-1); 
ic={y[-1]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {\int _{-1}^t\frac {3-K[1]}{K[1]-1}dK[1]}{t-3} \]

✓ Sympy. Time used: 0.276 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - 1/(t - 1) + y(t)/(t - 3),0) 
ics = {y(-1): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t - 2 \log {\left (t - 1 \right )} + 1 + 2 \log {\left (2 \right )} + 2 i \pi }{t - 3} \]