Question

For the system ?? ?? = −2? ?? ?? = 1 2 ? with ?(0) =...

For the system ?? ?? = −2? ?? ?? = 1 2 ? with ?(0) = 0, and ?(0) = 1 .

a) Show that (?(?), ?(?)) = (−2 sin(?) , cos(?)) is the solution to the initial value problem.

b) Use Euler’s Method with a step size of Δ? = 0.1 to find an approximate solution.

Find the approximate values at ? = 5, 10, and 20. That is, if ?(?) represents the approximation to ?(?), and ?(?) represents the approximation to ?(?), from Euler’s method then give (round to 10 decimal places):

(?(5), ?(5)) =

(?(10), ?(10)) =

(?(20), ?(20)) =

Please show steps and explain clearly. i need to progress my understanding

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