90.4.4 problem 4 and 5

Internal problem ID [25099]
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 59
Problem number : 4 and 5
Date solved : Thursday, October 02, 2025 at 11:50:10 PM
CAS classification : [_linear]

\begin{align*} t y^{\prime }+y&={\mathrm e}^{t} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 15

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

\[ y = \frac {{\mathrm e}^{t}-{\mathrm e}}{t} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to \frac {e^t-e}{t} \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = \frac {e^{t} - e}{t} \]