Question

Consider the equation: x'=x^3-3x^2+2x sketch the phase line. solve the equation and sketch the graphs of...

Consider the equation:

x'=x^3-3x^2+2x

sketch the phase line. solve the equation and sketch the graphs of some solutions including at least one solution with values in each interval above, below and between the critical points.

identify critical points as stable or unstable

Homework Answers

Answer #1

If you have any doubt, then please let me know in the comment.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the equation x'= x3 - 3x2 + 2x. Sketch the phase line. Solve the equation...
Consider the equation x'= x3 - 3x2 + 2x. Sketch the phase line. Solve the equation and sketch the graphs of some solutions including at least one solution with values in each interval above, below and between the critical points. Identify the critical points as stable or unstable.
For the autonomous differential equation dy/dt=1-y^2, sketch a graph of f(y) versus y, identify the equilibrium...
For the autonomous differential equation dy/dt=1-y^2, sketch a graph of f(y) versus y, identify the equilibrium solutions identify them as stable, semistable or unstable, draw the phase line and sketch several graphs of solutions in the ty-plane.
] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 ....
] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 . Sketch a graph of f(y) by hand and use it to draw a phase line. Classify each equilibrium point as either unstable or asymptotically stable. The equilibrium solutions divide the ty plane into regions. Sketch at least one solution trajectory in each region.
Consider the autonomous first-order differential equation dy/dx=4y-(y^3). 1. Classify each critical point as asymptotically stable, unstable,...
Consider the autonomous first-order differential equation dy/dx=4y-(y^3). 1. Classify each critical point as asymptotically stable, unstable, or semi-stable. (DO NOT draw the phase portrait and DO NOT sketch the solution curves) 2. Solve the Bernoulli differential equation dy/dx=4y-(y^3).
1. solve for x and graph solutions on a real number line -7≤ 2x+5≤21 2. Solve...
1. solve for x and graph solutions on a real number line -7≤ 2x+5≤21 2. Solve for x and graph solution on a real number line |7-3x|>2 3. write without absolute value and do not replace radical with decimal representation: |4- radical 17| 4. Solve for x and check | 2x-11 | =31 Side note* | means absolute value for 4 its absolute of 4- radical 17 and then absolute
Solve the ODE: ( 3x^2 − 4xy − 3 ) + ( − 9y^2 − 2x^2...
Solve the ODE: ( 3x^2 − 4xy − 3 ) + ( − 9y^2 − 2x^2 + 3 )y' = 0 . Entry format: Write your solution equation so that: (1) The equation is in implicit form. (2) The highest degree term containing only x has a coefficient of 1. (3) Constants are combined and moved to the RHS of the equation. _____________________= C
3. Given the function ?(?) = (x^3/3)-(3x^2/2)+2x: a. Find all critical numbers. b. Identify which, if...
3. Given the function ?(?) = (x^3/3)-(3x^2/2)+2x: a. Find all critical numbers. b. Identify which, if any, critical numbers are local max or min and explain your answer. c. Find any inflection points and give the x value. d. On the interval [0.6, 2.6] identify the absolute max and min, if any. and justify your answer. e. Give the interval where the curve is concave up and justify your answer.
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...
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.
(b) Solve the separable differential equation                   y'= (7e^-3x+2x^2-xcosx)/-6y^3             &nb
(b) Solve the separable differential equation                   y'= (7e^-3x+2x^2-xcosx)/-6y^3                                              (c) Solve the IVP              x(1-siny)dy=(cosx-cosy-y)dx .                              y(π/2)=0