Question

+0.5/1 points Previous AnswersSCalcCC4 7.2.001 2, 9x cos(Ty) is shown A direction field for the differential equation y y 2.0 1.5 1.0 0.5 0.4 -0.6 -0.4 -0.2 0.0 0.2 0.6 (a) Sketch the graphs of the solutions that satisfy the given initial conditions. (i) y(0) 0 (iii y(0) 1 (ii) y(0) 0.5 (iv) y(0) 1.6 V y 2:0 1.5 1.5 .5 X -0.6 O-0.6 -0.2 -0.4 0.6 -0.4 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4 2.0r 1.5 1.5 0.5 x 0.6 بسبــتـــاميد x -0.6 -0.4 -0.2 0.0 0.2 0.4 O-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 (b) Find all the equilibrium solutions. (Select all that apply.) y 0 y 0.5 y 1 y 1.5 y= 2

Answer 1

a) The answer is the top right picture because the curves have to cross the y-axis at y=0, y=0.5, y=1 and  y=1.6

b) The equilibrium solutions are the solutions whose slope is constant and equal to 0.

(horizontal lines in the direction field)

Therefore the equilibrium solutions are

y= 0.5

y=1.5