90.4.1 problem 1

Internal problem ID [25096]
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 : 1
Date solved : Thursday, October 02, 2025 at 11:50:05 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 3 y+y^{\prime }&={\mathrm e}^{t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 15

ode:=diff(y(t),t)+3*y(t) = exp(t); 
ic:=[y(0) = -2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{t}}{4}-\frac {9 \,{\mathrm e}^{-3 t}}{4} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 21

ode=D[y[t],{t,1}]+3*y[t] ==Exp[t]; 
ic={y[0]==-2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{4} e^{-3 t} \left (e^{4 t}-9\right ) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) - exp(t) + Derivative(y(t), t),0) 
ics = {y(0): -2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {e^{t}}{4} - \frac {9 e^{- 3 t}}{4} \]