90.25.4 problem 4

Internal problem ID [25385]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 379
Problem number : 4
Date solved : Friday, October 03, 2025 at 12:00:47 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t) = exp(-3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (-3 t -3 c_1 -1\right ) {\mathrm e}^{-3 t}}{9}+c_2 \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to c_2-\frac {1}{9} e^{-3 t} (3 t+1+3 c_1) \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{1} + \left (C_{2} - \frac {t}{3}\right ) e^{- 3 t} \]