74.3.3 problem 1 (c)

Internal problem ID [15792]
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 : 1 (c)
Date solved : Monday, March 31, 2025 at 01:49:32 PM
CAS classification : [_linear]

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

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

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

\[ y = \left ({\mathrm e}^{-1} \operatorname {Ei}_{1}\left (-1+t \right )+c_1 \right ) {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 33

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

\[ y(t)\to e^t \left (\int _1^t-\frac {e^{-K[1]}}{K[1]-1}dK[1]+c_1\right ) \]

✓ Sympy. Time used: 2.998 (sec). Leaf size: 36

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

\[ \int \frac {e^{- t}}{t - 1}\, dt + \int \frac {y{\left (t \right )} e^{- t}}{t - 1}\, dt - \int \frac {t y{\left (t \right )} e^{- t}}{t - 1}\, dt = C_{1} \]