Question: 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

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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