6, (9 marks) For each of the following direction field plots, write down a function f(t....
makes) For each of the following direction field plots, write down a function f(ty) such that! the differential equation dy = f(t,y) could have this direction field. In each case, give reasons why you think your differential equation could have the direction field shown. + + + to TTTTTTT 1 1 1 1 - 111111111111 PTT TTT 1 1 1 1 1 1 1 1 1 1 1 1 1 UTILIITTI 1 1 1 1 1 1 1 1 III...
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
3. Draw the direction field of the following differential equation: = (1-y)y dt What happens for the solution satisfying y(0)-2, 1, 0.5,-1 as t-> oo? If y(2)-β and limt→oo y(t) = 1. Find all possible values of β.
Can you explain drawing a direction field for this please? Its
not supoosed to be solved but rather shown through a direction
field that the limit as it approaches infinity is infinity.
1. 5 pts. Consider the differential equation dy (y-1)(y-2)2 dt Determine limo y (t) if y(0) need to solve the equation. 1.5 (it's possible that this imit is oo or -o0). You do not
dy The slope field below is that for some differential equation = f(t, y) 1 1 1 1 1 2 From this, give a possible solution to the differential equation y 42-1-\3A.
solve please
8 Sketch the direction field of the differential equation dx dt Verify that x t-1 Ce is the solution of the equation. Sketch the solution curve for which x(0) 2, and that for which x(4) 0, and check that these are consistent with your direction field. MAPI R has tools for exam
8 Sketch the direction field of the differential equation dx dt Verify that x t-1 Ce is the solution of the equation. Sketch the solution curve...
need help with these, plus checking if valid? please show
work!
28) The differential equation with the given direction field has 0.5 and 1.5 as equilibria A) 0.5 is unstable and 1.5 is locally stable B)1.5 is unstable and 0.5 is locally stable C) both are unstable D) both are locally stable R 29) Find the volume of the solid generated by revolving the region bounded by y 2x+3 and y=0, between x 0 and x ANT 1 about the...
Consider the system of linear differential equations z,(t)-17/11 z(t) + 9/11 y(t) y,(t)-18/11 z(t) + 38/11 y(t) a) Find the equation of the x-nullcline. Write your answer as an equation in z and y Answer b) Find the equation of the y-nullcline. Write your answer as an equation of z and y Answer. c) The nullclines divide the plane into four regions as illustrated below. 忽聡 2 -2 2 -2 For each of the regions, determine the direction of the...
9. (a) Find the inverse Fourier transform of the following function 1 (2 iw)(5 iw) (b) The displacement of a particular mechanical system is governed by the following ordinary differential equation dy 10y f(t) 7 dt where y(t) is the displacement and f(t) is the applied load Page 2 of 4 MATH2124 SaMplE EXAM IV i Use the Fourier transform to obtain the impulse response h(t) of the mechanical system (ii) If the applied load is f(t) = H (t1)-...
Consider the differential equation y′ = 3y − 9. (a) (1 pt) Make a direction field plot for this function which includes the point (t, y) = (0, 2). (b) (2 pts) Solve the equation by dividing 3y − 9 and using the method outlined in Section 1.2. (c) (1 pt) Find the solution which corresponds to y(0) = 2. (d) (1 pt) Plot the solution corresponding to y(0) = 2 on your direction field plot.
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s). b) Create an appropriate table of values and then sketch (using the grid provided) a direction field for this differential equation on OSIS 3. Be sure to label values on your axes. c) Using the direction field, describe in detail the behavior of y ast approaches infinity. 2. Short answer: State whether or not the differential equation is linear. If it is linear, state...