Section 5.3: Find the equilibrium values of a general quadratic population model: dx/dt=a1x+b1x^2+c1xy dy/dt=a2y+b2y^2+c2xy Don’t forget...

Section 5.3: Find the equilibrium values of a general quadratic population model:

dx/dt=a1x+b1x^2+c1xy

dy/dt=a2y+b2y^2+c2xy

Don’t forget to show this for all four cases:

Case 1: ? = 0, ? = 0
Case 2: ? ≠ 0, ? = 0
Case 3: ? = 0, ? ≠ 0
Case 4: ? ≠ 0, ? ≠ 0 (Use Cramer’s Rule to set up the solution for this case.)

Expert Solution

Please upvote me dear. God bless you.

Colby Messinger answered 1 year ago

dx dt =ax+by dy dt =−x − y, 2. As the values of a and b...

dx dt =ax+by dy dt =−x − y, 2. As the values of a and b are changed so that the point (a,b) moves from one region to another, the type of the linear system changes, that is, a bifurcation occurs. Which of these bifurcations is important for the long-term behavior of solutions? Which of these bifurcations corresponds to a dramatic change in the phase plane or the x(t)and y(t)-graphs?

Find the general solution of the given system. dx dt = 6x + y dy dt...

Find the general solution of the given system. dx dt = 6x + y dy dt = −2x + 4y [x(t), y(t)]= _____________, _______________ (6c1+8c2)10sin(6t)+(6c2+8c1)10cos(6t), c1cos(6t)+c2sin(6t) ^above is the answer I got, which is incorrect.

Find the general solution of the given system. dx/dt=6x-y dy/dt=5x+4y

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

Find the general solution: dx/dt + x/(1+2t) = 5

Find the general solution of this ODE: d^2y/dt^2+7 dy/dt+10y=5t^2−3t+6 The solution will be of the form:...

Find the general solution of this ODE: d^2y/dt^2+7 dy/dt+10y=5t^2−3t+6 The solution will be of the form: y(t)=Cy1(t)+Dy2(t)+yp(t) so use C and D as the arbitrary constants. y(t)=y(t)=

Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5

If a population with harvesting rate h is modeled by dx/dt = 9-x^2-h. Find the bifurcation...

If a population with harvesting rate h is modeled by dx/dt = 9-x^2-h. Find the bifurcation point for the equation.

Find dy/dx and d^2y/dx^2, and find the slope and concavity (if possible) at the given value...

Find dy/dx and d^2y/dx^2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.) Parametric Equations Point x = et, y = e−t t = 3 dy/dx = d^2y/dx^2 = slope = concavity= ---Select--- concave upward concave downward neither

1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2. x...

1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them at t = 2. x = t^2 , y= t ln t 2) Find the arc length of the curve on the given interval. x = ln t , y = t + 1 , 1 < or equal to t < or equal to 2 3) Find the area of region bounded by the polar curve on the given interval. r = tan theta , pi/6 < or...

Question