From the following list of differential equations, identify the right alternative that describes best the given direction field shown in the figure. a. y = y(y - 3) Ob Od O a y 3 b.y' = 2y - 1 c. y'=y (3-y) d. y' = y(y + 3) e. None For 0 < y 3, what we can say about the direction field is representing in the figure? y 5 O The solution diverge from y=0 O The solution converge to y = 0 O None of the above O The solution diverge from y = 3 O The solution converge to y = 3 Find the solution of the initial value problem differential equation. Then describe how the solution behaves as t . O A A. y = /2 + (yo /2) e-7t, as t, the solution converges to y = 2. B. y = + (yo ) e-7t, 1/72. ast , the solution converges to y = - ast , the solution diverges. D. y = 2/2 + (yo 2) e-7t, ast , the solution diverges. C. y = + (yo) et, E. None of the above O C OB dy = -7y + 2, dt OD y (0) = yo For the given differential equation, its general solution and behavior of y as t are, y = 1 + 2y A.y = 1/2 + cet, B. y = - + cet, as t , y- as t , y C.y=+cet, as t D.y = - + cet, as t E. None of the above O C O A OD OB , y , y HIN - A radioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the dQ d.t amount currently present. If Q(t) is the amount present at time t, then -rQ, where r > O is the decay rate. If 100 mg of thorium-234 decays to 82.04 mg in 1 week, find an expression for the amount of thorium-234 present at any time t and the value of the decay rate r. A. Q (t) = 82.04e-rt, B. Q (t) = 100e-rt, C. Q (t) = 10e-rt D. Q (t) = 100et, E. None of the above OD O A OB C " r = r = r = r = 0.198 week 0.198 week 0.98 week 0.198 week Determine the order of the given differential equations (DE) and state whether the equation is linear or nonlinear. So, match the letter representing the DE on the left with your classification on the right side. A. A B.y" +(x + y) y' - 6y = x C. y" + (cos x) y' - 3xy = ex D. y' + (y') y = 0 B C (dv) D 3 dy + + y = sin x dx Second order DE, nonlinear Third order DE, linear Third order DE, nonlinear Second order DE, linear