Consider the logistic equation p' = 2(1 – 100)p. If p(t) is a solution to the...
2. Suppose a population P(t) satisfies the logistic differential
equation dP dt = 0.1P 1 − P 2000 P(0) = 100 Find the following: a)
P(20) b) When will the population reach 1200?
2. Suppose a population P(t) satisfies the logistic differential equation 2P = 0.1P (1–2000) = 0.1P | P(0) = 100 2000 Find the following: a) P(20) b) When will the population reach 1200?
Find the general solution of the equation y" + 361y = 0. y(t) = C1 cos 19t + c2 sin 19t o o o o y(t) = ci cos t-cı sin t y(t) = ci cos t+ c2 sin 19t y(t) = cı cos 19t+ c2 sin t
(1 point) Consider the logistic equation y = y(1 - y) (a) Find the solution satisfying y(0) = 8 and yz (0) = -4. yı(t) = y2(t) (b) Find the time t when yı(t) = 4. t (c) When does yz(t) become infinite?
Consider the following logistic equation for t2 0. Sketch the direction field, draw the solution curve for each initial condition, and find the equilibrium solutions. Assume t20 and P0. P P' (t) = 0.02P 1- 300 P(O) = 100, P(O) = 200, P(O) = 400 OA P 1000 OB P 1000 O c. P 1000 OD P 1000 750 750 750 750 500 500 500 500 250 2501 250 250 100 200 300 400 100 200 300 400 100 200...
please solve this question
1. Consider the following modified Logistic model to describe a population p -p(t) with stronger competition as time t increases: dys Here the net birth rate is 1 and the competition term is (1 - e ')p with constant a > 0 (a) Make a substitution of the form u p for some integer m and so reduce (1) to the linear first Cl order o.d.e du dt (b) Find the general solution of (1) (c)...
Q1/ Consider the modified logistic population growth equation P = Pla-bP) + ce-P Here, and k are positive constants. The additional term ce represents the immigration. Clearly, the immigration is less when the population is large than when it is small. This decrease may be caused, for example, by the imposition of quotas, or by overcrowding of the region and a resulting deterioration of the favorable conditions that had attracted immigrants. Use Runge Kutta method to find the solution of...
part d please
We go back to the logistic model for population dynamics (without harvesting), but we now allow the growth rate and carrying capacity to vary in time: dt M(t) In this case the equation is not autonomous, so we can't use phase line analysis. We will instead find explicit analytical solutions (a) Show that the substitution z 1/P transforms the equation into the linear equation k (t) M(t) dz +k(t) dt (b) Using your result in (a), show...
true or false
If yı(t) and y2(t) are two solutions of the differential equation y2 – y' +y = 0, then for any constants cı and c2, cıyı(t) + C2y2(t) is also a solution. Doğru Yanlış
(Problem 2:) (1) What is the general solution of the logistic equation, dN (a – bN)N? dt (2) Given that No = 3, a = ..001, calculate the carrying capacity. (3) Sketch the solution as t+00. (4) Calculate the doubling time tlog. Compare this doubling time with the doubling time texp of the exponential growth model: ON = aN with No = 3 and a = = .05. .05, b
Differential Equations
Problem 3. Background. The Gompertz logistic equation is dP (P) -P(a-b In P) where a, b are positive constants. dP This model is similar to the usual logistic model, which can be written ab P). f(P)- P(a-b InP) is defined for all P>0. Also, since lim fP)-0,we extend the definition of f(P) so that f(O) Problem 3. a. Verify (by L'Hopital's rule) that lim f(P)-0 b. Show that, if we set B-e, then we can write the equation...