90.4.15 problem 16

Internal problem ID [25110]
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 : 16
Date solved : Thursday, October 02, 2025 at 11:50:27 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(y(t),t)+a*y(t) = exp(-a*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (t +c_1 \right ) {\mathrm e}^{-a t} \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to e^{-a t} (t+c_1) \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 10

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

\[ y{\left (t \right )} = \left (C_{1} + t\right ) e^{- a t} \]