For the following differential equations: a) plot the defining function over the indicated range (use any computational tools you wish) to determine the intervals on which the dependent variable is increasing and decreasing; b)
For the following differential equations: a) plot the defining function over the indicated range (use any computational tools you wish) to determine the intervals on which the dependent variable is increasing and decreasing; b) find the equilibria c) determine the stability of each equilibrium; d) based on your analysis in parts a-c, sketch (by hand) plots of the solutions with the specified initial values.
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dC / dt = −0.2C + 60; C ∈ (0,500); C(0) = 200; C(0) = 400
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dP / dt = 0.01P(800 − P) − 0.5P; P ∈ (−1,1000); P(0) = 100; P(0) = 800
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dR / dt = R(80 − R) − 1200; R ∈ (−1,100); R(0) = 10; R(0) = 80
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dI / dt = 0.1I(1 − I) − 0.03I; I ∈ (−0.1,1.1); I(0) = 0.2; I(0) = 0.9
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