37.1.1 problem 10.2.4

Internal problem ID [6388]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page 307
Problem number : 10.2.4
Date solved : Monday, January 27, 2025 at 01:58:40 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-\omega ^{2} x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(x(t),t$2)-omega^2*x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = c_1 \,{\mathrm e}^{\omega t}+c_2 \,{\mathrm e}^{-\omega t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

DSolve[D[x[t],{t,2}]-\[Omega]^2*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to c_1 e^{t \omega }+c_2 e^{-t \omega } \]