The amounts x, (t) and x2(t) of salt in two brine tanks satisfy the differential equations below, r for i = 1, 2. The volumes are V, Vi where k; = 40 (gal) and V, = 20 (gal). First solve for x4 (t) and x2(t) assuming that r= 6 (gal/min), x, (0) = 12 (Ib), and x2(0) = 0. Then construct a figure showing the graphs of x, (t) and x, (t). %3D dx, - k,x1 + k2X2, dx2 = kqx1 - k2x2 dt dt X1 (t) = X2 (t) = Choose the correct graph of x, (t) and x2(t) below. OA. В. С. D. Ax 12- 12- 12- 12- X1 X. 0- 04

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.