Internal problem ID [4537]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {x^{\prime \prime }-\omega ^{2} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 18
dsolve(diff(x(t),t$2)-omega^2*x(t)=0,x(t), singsol=all)
\[ x \relax (t ) = c_{1} {\mathrm e}^{-\omega t}+c_{2} {\mathrm e}^{\omega t} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 23
DSolve[x''[t]-\[Omega]^2*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{t \omega }+c_2 e^{-t \omega } \\ \end{align*}