Mathematics
First Course Differential Equations
The amounts x 1 (t) and x 2 (t) of

The amounts x 1 (t) and x 2 (t) of salt in the two brine tanks of Fig. 7.3.8 satisfy

Question:

The amounts x₁(t) and x₂(t) of salt in the two brine tanks of Fig. 7.3.8 satisfy the differential equations

where k_i = r/ V_i as usual. In Problems 29 and 30, solve for x₁ (t) and x₂ (t), assuming that r = 10 (gal/min), x₁ (0) = 15 (lb), and x₂ (0) = 0. Then construct a figure showing the graphs of x₁ (t) and x₂ (t).

V₁ = 50 (gal), V₂ = 25 (gal)

Transcribed Image Text:

dx1 dt = -k1x1 + k2x2, dx2 dt = k₁x1-k2x2,

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