38.2.7 problem 7

Internal problem ID [8225]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 05:19:13 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (0\right )&=-1 \\ x^{\prime }\left (0\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 13

ode:=diff(diff(x(t),t),t)+x(t) = 0; 
ic:=[x(0) = -1, D(x)(0) = 8]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 8 \sin \left (t \right )-\cos \left (t \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 14

ode=D[x[t],{t,2}]+x[t]==0; 
ic={x[0]==-1,Derivative[1][x][0] == 8}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 8 \sin (t)-\cos (t) \end{align*}

✓ Sympy. Time used: 0.031 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): -1, Subs(Derivative(x(t), t), t, 0): 8} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = 8 \sin {\left (t \right )} - \cos {\left (t \right )} \]