74.19.10 problem 10

Internal problem ID [16632]
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 : Tuesday, January 28, 2025 at 09:13:33 AM
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*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 17

dsolve([10*diff(x(t),t$2)+1/10*x(t)=0,x(0) = -5, D(x)(0) = 1],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

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

\[ x(t)\to -5 \left (\cos \left (\frac {t}{10}\right )-2 \sin \left (\frac {t}{10}\right )\right ) \]