2. In these problems, determine a differential equation of the form dy/dt = ay+b whose solutions...
So derive (by hand) the closed-form solutions to the following three problems using this approach: dy (a)| +5y= 6 cos(t) sin(t); y(0)=5 (b) | dy-y=cos2(t): y(0)=1 dy sin 0 (c)-+ 3y ;y(0) = 2 dt 2S1
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...
In this problem we consider an equation in differential form M dx + N dy = 0. (4x4 + 2y) dx +(- (2x + y2))dy = 0 Find My Nx = = If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) solutions to the differential equation. C, give implicit general If the equation is not exact, enter NE otherwise find...
3. Find all a,b such that all solutions of the differential equation y+ ay+by 0 converge to zero asgoes to
Find a differential equation whose solution is: 30. Find a 1-parameter family of solutions of the differential equation dy - y dz and the particular solution for which y(3) -
Consider the differential equation dy -0.5y (y – 4) dt Question 1 Why is the given differential equation considered autonomous?" The derivative of the unknown function(y) is described only in terms of y, not t. The derivative of the unknown function (y) is a first derivative, not a second derivative. The derivative of the unknown function(y) is described only with linear factors such as -0.5y and (y-4), not curves such as sin(y) or 1/y. Question 2 As a step toward...
Solve the following differential equation using variation of parameters. d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3 d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...