Integrate the differential equation [-frac{d^{2} x}{d t^{2}}+0.1 x=0 quad text { for } quad 0 leq t
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Integrate the differential equation
\[-\frac{d^{2} x}{d t^{2}}+0.1 x=0 \quad \text { for } \quad 0 \leq t \leq 10\]
using the backward difference formula with \(\Delta t=1\). Assume the initial conditions as \(x_{0}=1\) and \(\dot{x}_{0}=0\).
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