Question

following nonlinear system: x' = 2 sin y, y'= x^2 + 2y − 1 find all...

following nonlinear system:

x' = 2 sin y,

y'= x^2 + 2y − 1

find all singular points in the domain x, y ∈ [−1, 1],determine their types and stability.

Find slopes of saddle separatrices.

Use this to sketch the phase portrait in the domain x, y ∈ [−1, 1].

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given a nonlinear system   x(t)" + cx(t)' + sin(x(t)) = 0                       (3-1) a) Consider its phase...
Given a nonlinear system   x(t)" + cx(t)' + sin(x(t)) = 0                       (3-1) a) Consider its phase plane by assuming proper parameters of c. Do you have singular points with the cases of CENTER FOCUS, NODE and SADDLE ? Are those stable? asymptotic stable or unstable? b) When c = 0, plot the phase plane and find these singular points
Consider the following nonlinear system: x'(t) = x - y, y'(t) = (x^2-4)y a. Determine the...
Consider the following nonlinear system: x'(t) = x - y, y'(t) = (x^2-4)y a. Determine the equilibria. b. Classify the equilibria using linearization. c. Use the nullclines to draw the phase portrait. Please write neatly. Thanks!
Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2. (i) Find the stationary...
Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2. (i) Find the stationary points of f. (ii) For each stationary point P found in (i), determine whether f has a local maximum, a local minimum, or a saddle point at P. Answer: (i) (0, −2), (2, 1), (−2, 1) (ii) (0, −2) loc. max, (± 2, 1) saddle points
Please draw a phase diagram of the system: x' = 6x - x^2 - xy y'...
Please draw a phase diagram of the system: x' = 6x - x^2 - xy y' = -2y + xy The critical points are and their type are: (0,0) unstable saddle (6,0) unstable saddle (2,4) stable/asympotically satble spiral
Consider the nonlinear second-order differential equation 4x"+4x'+2(k^2)(x^2)− 1/2 =0, where k > 0 is a constant....
Consider the nonlinear second-order differential equation 4x"+4x'+2(k^2)(x^2)− 1/2 =0, where k > 0 is a constant. Answer to the following questions. (a) Show that there is no periodic solution in a simply connected region R={(x,y) ∈ R2 | x <0}. (Hint: Use the corollary to Theorem 11.5.1>> If symply connected region R either contains no critical points of plane autonomous system or contains a single saddle point, then there are no periodic solutions. ) (b) Derive a plane autonomous system...
Consider the linear first order system [16] x′ = x + y (1) y′ =4x−2y. (2)...
Consider the linear first order system [16] x′ = x + y (1) y′ =4x−2y. (2) (a) Determine the equilibria of System (1)-(2) as well as their stability. [6] (b) Compute the general solution of System (1)-(2). [6] (c) Determine the solution of the initial value problem associated with System (1)-(2), with initial condition x(0) = 1, y(0) = 2.
a) Find the domain and range of the following function: f(x,y)=sin(ln(x+y)) b) sketch the domain. c)...
a) Find the domain and range of the following function: f(x,y)=sin(ln(x+y)) b) sketch the domain. c) on seperate graph, sketch three level curves
Consider the non linear system X dot = y + x(x^2 + y^2 - 1) *...
Consider the non linear system X dot = y + x(x^2 + y^2 - 1) * sin 1 /x^2 + y^2 - 1 Y dot = - x + y(x^2 + y^2 - 1) * sin 1/ x^2 + y^2 - 1 Without solving the above equations explicitly, show that the system has infinite number of limits cycles. Determine the stability of these limit cycles (Hint : Use polar coordinates)
Let f (x, y) = 100 sin(π(x−2y))/(1+x^2+y^2) . Find the directional derivative of f 1+x^2+y^2 at...
Let f (x, y) = 100 sin(π(x−2y))/(1+x^2+y^2) . Find the directional derivative of f 1+x^2+y^2 at the point (10, 6) in the direction of: (a) u = 3 i − 2 j (b) v = −i + 4 j
Given dy/dx =y(y−3)(1−y)^2 dx (a) Sketch the phase line (portrait) and classify all of the critical...
Given dy/dx =y(y−3)(1−y)^2 dx (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point). (b) Next to your phase line, sketch the graph of solutions satisfying the initial conditions: y(0)=0, y(0)=1, y(0)=2, y(0)=3, y(2)=4, y(0)=5.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT