68.19.10 problem 10

Internal problem ID [17919]
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 : 10
Date solved : Thursday, October 02, 2025 at 02:29:47 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 10 x^{\prime \prime }+\frac {x}{10}&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=-5 \\ x^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 17

ode:=10*diff(diff(x(t),t),t)+1/10*x(t) = 0; 
ic:=[x(0) = -5, D(x)(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 10 \sin \left (\frac {t}{10}\right )-5 \cos \left (\frac {t}{10}\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

ode=10*D[x[t],{t,2}]+1/10*x[t]==0; 
ic={x[0]==-5,Derivative[1][x][0 ]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -5 \left (\cos \left (\frac {t}{10}\right )-2 \sin \left (\frac {t}{10}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.039 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t)/10 + 10*Derivative(x(t), (t, 2)),0) 
ics = {x(0): -5, Subs(Derivative(x(t), t), t, 0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = 10 \sin {\left (\frac {t}{10} \right )} - 5 \cos {\left (\frac {t}{10} \right )} \]