7. Determine the equilibrium points of y-y(y-1)。") and elasify each one. Sketch the graphs of the...
7. Determine the equilibrium points of y-y(y-1)。") and elasify each one. Sketch the graphs of the integral curves with initial values: y(0) =-9, y(0) = 0, y(0) =-0.4, y(0) = 1, and y(0-5.[Spoints1 7. Determine the equilibrium points of y-y(y-1)。") and elasify each one. Sketch the graphs of the integral curves with initial values: y(0) =-9, y(0) = 0, y(0) =-0.4, y(0) = 1, and y(0-5.[Spoints1
4. Determine and classify each one of the equilibrium points of y' (y -2) sin y. Sketch the graphs of the integral curves with initial values: y(0) =-T, y(0)--π/2, y(0) = 0, y(0) = π/2, y(0) = 2, y(0) = 3, y(0) = π, and y(0) 4. Label them clearly.
Using Differential Equations. 6. For y, = y3 _ y, y(0) = 30, -00 <30 < 00, draw the graph of (y) = y3-y versus y, determine the equilibrium solutions (critical points) and classify each one as unstable or asymptotically stable. Draw the phase line, and sketch several representative integral curves (graphs of solutions) in the (t, y) plane. Hint: None of this requires explicit formulas for solutions y = φ(t) of the initial value problem.]
7. Use the graphs of ſand g to sketch the parametric curve x = f(0, y = g(). Indicate the direction of motion and the initial and terminal points. 2f0 4
1. Sketch each of the components of the following signals on the graphs provided. Sketch and highlight the resultant signals on the same graphs as well. (a) xy(t)=u(t+1)-u(1-1) (5 points) Ixl(t) . : + ---. t +--+ -3 + -2 + -1 0 1 2 (b) x2(t)=r(t +2) - 2r(t+1)+r(t) (5 points) + + + + + + + + + + + + + + + + 4 + + + + + + + + 3+ + +...
dP 7. For the equation = (P+2)(P2 - 6P+5)find the equilibrium points and make a phase dt portrait of the differential equation. Classify each equilibrium point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves determined by the graphs of equilibrium solutions. (6pts)
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
7. Answer the questions below for the following initial value problem: y (t) = sin y, 0 <y(0) < 27. (a) [1 pt) Determine the equilibrium (i.e., critical or steady-state) solutions. (b) (2 pts) Construct a sign chart for y' = sin y. Hy' = sin y 21 (c) (3 pts] Now construct a sign chart for y", and find the inflection points (if any). Hy" = f(y) 271 (d) [5 pts] Draw the phase line, and sketch a graph...
use the direction field labeled III above to sketch the graphs of Use the direction field labeled III (above) to sketch the graphs of the solutions that satisfy the given initial con tions. (a) y(0) 1 (b) y(0)-2.5 (c) y(0) 3.5 Use the direction field labeled III (above) to sketch the graphs of the solutions that satisfy the given initial con tions. (a) y(0) 1 (b) y(0)-2.5 (c) y(0) 3.5
+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...