68.19.1 problem 1

Internal problem ID [17910]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 5. Applications of Higher Order Equations. Exercises 5.1, page 232
Problem number : 1
Date solved : Thursday, October 02, 2025 at 02:29:33 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 x^{\prime \prime }+9 x&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 10

ode:=4*diff(diff(x(t),t),t)+9*x(t) = 0; 
ic:=[x(0) = -1, D(x)(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -\cos \left (\frac {3 t}{2}\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 13

ode=4*D[x[t],{t,2}]+9*x[t]==0; 
ic={x[0]==-1,Derivative[1][x][0 ]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\cos \left (\frac {3 t}{2}\right ) \end{align*}

✓ Sympy. Time used: 0.037 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(9*x(t) + 4*Derivative(x(t), (t, 2)),0) 
ics = {x(0): -1, Subs(Derivative(x(t), t), t, 0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = - \cos {\left (\frac {3 t}{2} \right )} \]