Find the particular solution of the system dx1 dt Зx1 + X3, dx2 dt 9х1 — х2 + 2х з, dx3 = -9x1 + 4x2 - X3 dt that satisfies the initial conditions x1(0) = 0, x2(0) = 0, x3(0) = 17. The amounts x1 (t) and x2(t) of salt in the two brine tanks of Fig. 5.2.7 satisfy the differential equations dx1 = -k1x1, dt dx2 = k1x1 – k2x2, dt where k; = r/V; for i = 1, 2. In Problems 27 and 28 the vol- umes V1 and V½ are given. First solve for x1(t) and x2(t), as- suming that r = 10 (gal/min), x1 (0) = 15 (lb), and x2(0) = 0. Then find the maximum amount of salt ever in tank 2. Finally, construct a figure showing the graphs of x1(t) and x2(t).

Find the particular solution of the system dx1 dt Зx1 + X3, dx2 dt 9х1 — х2 + 2х з, dx3 = -9x1 + 4x2 - X3 dt that satisfies the initial conditions x1(0) = 0, x2(0) = 0, x3(0) = 17. The amounts x1 (t) and x2(t) of salt in the two brine tanks of Fig. 5.2.7 satisfy the differential equations dx1 = -k1x1, dt dx2 = k1x1 – k2x2, dt where k; = r/V; for i = 1, 2. In Problems 27 and 28 the vol- umes V1 and V½ are given. First solve for x1(t) and x2(t), as- suming that r = 10 (gal/min), x1 (0) = 15 (lb), and x2(0) = 0. Then find the maximum amount of salt ever in tank 2. Finally, construct a figure showing the graphs of x1(t) and x2(t).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.6: Applications Of Differential Equations

Problem 15E: Solve Exercise 14 if a 25 solution of the same mixture is added instead of pure alcohol.

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