QUESTION 1 a) Show that the following equation 2xy = 2x y?. dy dr is...
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QUESTION 1 a) Show that the following equation 2xy = 2x – y?. dy dr is an exact differential equation. Hence solve it. b) Use the substitution v = x +y +3 to solve the following initial value problem (x+ y + 3)%, dr y(0) = 0. c) Suppose glucose is injected into a patient's bloodstream at a constant rate of r units per unit of time. Let y = y(t) be the number of units of glucose in the patient's bloodstream at time t > 0 and A > 0 is a constant. Then dy -Ay +r, dt where the first term on the right is due to the absorption of glucose by the patient's body and the second term is due to the injection. i. Determine y(t) given that y(0) = yo- ii. How many units of glucose left in the body when t+ oo? QUESTION 1 a) Show that the following equation 2xy = 2x – y?. dy dr is an exact differential equation. Hence solve it. b) Use the substitution v = x +y +3 to solve the following initial value problem (x+ y + 3)%, dr y(0) = 0. c) Suppose glucose is injected into a patient's bloodstream at a constant rate of r units per unit of time. Let y = y(t) be the number of units of glucose in the patient's bloodstream at time t > 0 and A > 0 is a constant. Then dy -Ay +r, dt where the first term on the right is due to the absorption of glucose by the patient's body and the second term is due to the injection. i. Determine y(t) given that y(0) = yo- ii. How many units of glucose left in the body when t+ oo?
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Related Book For
Digital Signal Processing
ISBN: ?978-0133737622
3rd Edition
Authors: Jonh G. Proakis, Dimitris G.Manolakis
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