only full solution for c and d In a simplified model of tumour growth, the size y(t) of the tumour at time t is given by...
I need help with question #3 When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in years. 1. Solve for the equilibrium value(s) and determine their stability. Create a slope field for this differential equation. Use the slope field to sketch solutions for various initial values. 2. 3. Summarize the behavior of the solutions and how...
Use the solution you found in Part 1f to show that the Gompertz model can be rewritten as dP/dt=−λe^(−rt)P, where λ is a positive constant. j) Consider grouping the factors in the equation like this: dP/dt=-(λe^(-rt))P. Make an interpretation of this equation. In other words, what assumption about tumour growth would lead us to write down such an equation? k) Now consider grouping the factors in the equation like this: dP/dt=−λ(e^(-rt)P). Again, explain what assumption about tumour growth would lead...
#20 please and specifically c.) .... but with the initial conditions only being A= (1,-1) and D=(-1,2). For A, I got x(t)=e^(-4t) and y(t) = -e^(-4t). For D, I got x(t)= 3/4*e^(4t)-7/4*e^(-4t) and y(t)=1/4*e^(4t)+7/4*e^(-4t) 295 3.3 Phase Portraits for Linear Systems with Real Eigenvalues 20. The slope field for the system y 3 dx =2x +6y dt dy = 2x - 2y dt is shown to the right. (a) Determine the type of the equilibrium point at the origin. x...
I need help with these! 3. (1 point) a) Compute the general solution of the differential equation y"5 12y" 0 b) Determine the test function Y (t) with the fewest terms to be used to obtain a particular solution of the following equation via the method if undetermined coefficients. Do not attempt to determine the coefficients.5y 12y"2 10e-tesin(V3t) Spring 2011) 4. (1 point) Compute the general solution of the following differential equations dz dy dt ii)(1y iv) (z cos(y) +...
d 21. Consider the following IS-LM model: C = co +61 (Y – T) I = bo + b Y – bai M d¡Y – dzi Р M P Р a. where (b+c) <1 b. Derive IS equation. Derive and determine its sign. [5 points]- di di c. b. Derive LM equation. Derive and determine its sign. [5 points]- d. c. Assume that LM curve is ** dY t dY () M P =dY Solve for the equilibrium output and...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3 Lš where K, is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation KH = (1-d) * Kit It: where d is the depreciation rate. Every person saves share s of his income and, therefore, aggregate saving is St-s...
Q3p please with mathlab. 1) The growth of populations of organisms has many engineering and scientific applications. One of the simplest models assumes that the rate of change of the population p is proportional to the existing population at any time t: dp/dt = kp where k, is the growth rate. The world population in millions from 1950 through 2000 was 1950 1959 1960 1965 1970 1975 1980 1989 1990 19952000 P25602780 3040 3350 3710 4090 4450 4850 528056906080 ....
Using the Runge-Kutta fourth-order method, obtain a solution to dx/dt=f(t,x,y)=xy^3+t^2; dy/dt=g(t,x,y)=ty+x^3 for t= 0 to t= 1 second. The initial conditions are given as x(0)=0, y(0) =1. Use a time increment of 0.2 seconds. Do hand calculations for t = 0.2 sec only.
Consider the Solow growth model that we developed in class. Output at time t is given by the production function Y AK Lt, where A is total factor productivity, Kt is total capital at timet and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and Y, + 1, where Ct is consumption and I is investment at tim. Every agent saves s share of...
hellllllllllp please a) Verify that the function y = ?? + is a solution of the differential equation zy' +2y 4x? (x > 0). b) Find the value ofe for which the solution satisfies the initial condition (2) - 5. = Submit Question a) Verify that the function y=x? + с 2 is a solution of the differential equation ry' + 2y = 4x², (x > 0). b) Find the value of c for which the solution satisfies the initial...