74.19.1 problem 1

Internal problem ID [16623]
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 : Tuesday, January 28, 2025 at 09:13:01 AM
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*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 10

dsolve([4*diff(x(t),t$2)+9*x(t)=0,x(0) = -1, D(x)(0) = 0],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 13

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

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