68.9.6 problem 14

Internal problem ID [17469]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 14
Date solved : Thursday, October 02, 2025 at 02:24:27 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t)+9*y(t) = 0; 
ic:=[y(0) = 1, D(y)(0) = -3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\sin \left (3 t \right )+\cos \left (3 t \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 16

ode=D[y[t],{t,2}]+9*y[t]==0; 
ic={y[0]==1,Derivative[1][y][0] ==-3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \cos (3 t)-\sin (3 t) \end{align*}

✓ Sympy. Time used: 0.036 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): -3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \sin {\left (3 t \right )} + \cos {\left (3 t \right )} \]