68.1.14 problem 21

Internal problem ID [17081]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 21
Date solved : Thursday, October 02, 2025 at 01:42:48 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(diff(y(t),t),t)+9*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{-9 t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 19

ode=D[y[t],{t,2}]+9*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.080 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} e^{- 9 t} \]