1. The first order linear method workflow is described in dx + a(t)x = f(x) dt dx the table to the left. The key step is when i(t): dt dx i(t) dt . + i(t) α (ΐ)x = i(t)f(t) i(t)a(t)x(t) simplifies to (x(t)i(t)) , however if d we calculate this derivative using the product rule (x i(t)) = i(t)f(t) dt x i(t) = S i(t)f(t)dt + C d di a (x(t)i(t)) = i(t) + x(t); , we can see that this dt C di x = i(t) Si(t)f(t)dt + simplification only happens if a(t) * i(t). Solve i(t) dt this first order separable equation to derive the formula for i(t). i(t) =

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