Consider the second-order differential equation:  (d2x/dt2) + x (dx/dt) = sin x.  which option gives an equivalent system of first-order differential equations?  A. dx/dt = y,     dy/dt = -xy + sin x  B. dy/dx = t,     dy/dt = -xy + sin x.  C. dy/dt = x,     dx/dt = -xy + sin x.  D. dy/dt = y,     dx/dt = -xy + sin x.  E. dx/dt = y,     dy/dt = -y + cos x.

Consider the differential equation: dy/dx = y(3 - y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. f'(x)=y(3-y) Kin/5 -5 Density Length dy de -8 Step size 0.1 Ymas y (3-9) Input. ✔Solution A Solution B Solution C Solution D DCQ= AC: 2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. - 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other…

Which of the following systems of differential equations would dictate the rates of change of the salt concentration for the two-tank system shown below? 10 L/min 70 g/L VAL 14 L/min I 6 L/min OC A/= (1/VA) (10 × 70 + 6cg - 14CA), c_l= (1/V₂) (14c. – 16c) OC Al= (1/VA) (70 – 6cв - 14CA), CB= (1/VB) (14CA - 16CB) 16св) VB L C Al= (1/VA) (14CA CB/= (1/VB) (14CA - 16CB) 10 × 70 – 6cß), C Al= (1/VA) (10 × 70+ 16cB - 14CA), CB/= (1/VB) (14CA 10CB) 10 L/min

If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the equation todx = dt (a)?