4. Determine and classify each one of the equilibrium points of y' (y -2) sin y....
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
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
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. 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...
MATLAB HELP 3. (a) In one window, graph four different solutions to y 00 + 10y 0 + y = sin t by using different initial conditions. (Be sure that all four graphs are clearly visible in the window.) (b) Describe the apparent behavior of the solutions as t → ∞. 4. (a) Graph solutions to y 00 + a y = sin 3t, y(0) = 1, y 0 (0) = 1 for each of the values a = 9.5,...
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)....
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line. 4 Consider the autonomous differential equation y f(v)...
Determine the equilibrium, classify each equilibrium, draw a phase line. If y(0)=1 then lim y(t) = ? If y(0)=2 then what is the solution y(t) =? 3/3-4y Let dt 3/3-4y Let dt
Consider the system x'=xy+y2 and y'=x2 -3y-4. Find all four equilibrium points and linearize the system around each equilibrium point identifying it as a source, sink, saddle, spiral source or sink, center, or other. Find and sketch all nullclines and sketch the phase portrait. Show that the solution (x(t),y(t)) with initial conditions (x(0),y(0))=(-2.1,0) converges to an equilibrium point below the x axis and sketch the graphs of x(t) and y(t) on separate axes. Please write the answer on white paper...
consider the autonomous equation 2. Consider the autonomous equation y=-(y2-6y-8) (a) Use the isocline method to sketch a direction field for the equation (b) Sketch the solution curves corresponding to the following intitial conditions: (1) y(0) 1 (2) y(0) =3 (3) y(0)=5 (4) 3y(0) 2 (5) y(0) = 4 (c) What are equilibrium solutions, and classify its equilibrium them as: sink (stable), source, node. (d) What is limy(t) if y(0) = 6? too 2. Consider the autonomous equation y=-(y2-6y-8) (a)...