For the initial value problem presented in Exercise, perform the of the following tasks.
(i) Solve the initial value problem analytically.
(ii) Use the analytical solution from part (i) and the theory of limits to find the behavior of the function as t → +∞.
(iii) Without the aid of technology, use the theory of qualitative analysis presented in this section to predict the long term behavior of the solution. Does your answer agree with that found in part (ii)? Which is the easier method?
y' + 2y = 5, y(0) = 0
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