Consider the first order differential equation, (frac{d x_{1}}{d t}=-x_{2}), with an initial value (x(0)=10). With an integration
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Consider the first order differential equation, \(\frac{d x_{1}}{d t}=-x_{2}\), with an initial value \(x(0)=10\). With an integration step size of 0.1 seconds, determine the value of \(x(0.5)\) using
(a) Euler's method,
(b) the modified Euler's method.
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