Question: Please show me the steps to finding the solution. The amounts x, (t) and X2 (t) of salt in two brine tanks satisfy the differential

Please show me the steps to finding the solution.

The amounts x, (t) and X2 (t) of salt in two brine tanks satisfy the differential equations below, where k; = , for i= 1, 2. The volumes are V, = 75 (gal) and V2 = 25 (gal). First solve for x, (t) and X2(t) assuming that r = 15 (gal/min), x, (0) = 8 (lb), and X2(0) = 0. Then construct a figure showing the graphs of x, (t) and X2 (t). dx 1 dx2 dt -= -k1x1 + K2x2' dt - = K1X1 - K2x2 xy (t ) = X2(t) =

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