63.7.4 problem 1(d)

Internal problem ID [13123]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.2.3 Complex eigenvalues. Exercises page 94
Problem number : 1(d)
Date solved : Tuesday, January 28, 2025 at 04:53:33 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-12 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: 0.033 (sec). Leaf size: 23

dsolve([diff(x(t),t$2)-12*x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{2 \sqrt {3}\, t}}{2}+\frac {{\mathrm e}^{-2 \sqrt {3}\, t}}{2} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 31

DSolve[{D[x[t],{t,2}]-12*x[t]==0,{x[0]==1,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} e^{-2 \sqrt {3} t} \left (e^{4 \sqrt {3} t}+1\right ) \]