Consider the system: I’ – 41+y” = ť? I'+I+y' = 0 In the first blank: Write the second equation using the D notation. (Do not put any spaces in your answer) In the second blank: Solving the system, we get Ic(t)- (use c1, c2, etc for our constants.) In the third blank: What is the form of p(t)? Xp In the forth blank: What is the final form of the 2p(t) portion of the system after you solve for your...
Using matrix algebra, find a general solution to the following system of equations x' = 3x - 4y and y' = 4x - 7yUsing matrix algebra, find a general solution to the following system of equations: x' = 3x - 4y y' = 4x - 7y The general solution functions are: ( use c1 and c2 as the constants and enter the elements of the eigenvectors as the lowest integer values. If one element of an eigenvector has a negative value enter the first element...
Consider the curve X = 42 y=ť, 0 <t<1 Setup the integral for the area of the surface obtained by rotating the curve about 27 (2+4 + 3t") dt [ 26 (28 + 3t) dt 2*t* 4 +01+ dt 27tº /2 + 3* dt [ 2013 (4+9t? dt
Express the system of differential equations in matrix notation x – 4x + y - (cos t)x = 0 y"+y" - t?x' + 3y'+e-2x = 0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. Xi =X, X2 = X". X3 = y, Xa =y" O B. *= x, X2 = x', *3 = y, X4 =y', X5 =y" OC. *1 =...
In Problems 41 , use the Laplace transform to solve each system. 41 x' + y=t 4x+y'=0 x(0,-1, y(0)-2 41 x' + y=t 4x+y'=0 x(0,-1, y(0)-2
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
Consider the nonlinear system: - x + (x – 1) y y + 4x° (1 – x). (a) Show that the system has a unique fixed point at the origin (0, 0). (b) Use a linear approximation to determine the stability of the fixed point. (c) Apply the Liapunov direct method to determine the stability of the fixed point. Is your conclusion different form that of Part (a)? Why? (d) Can the system have closed orbits (trajectories)? Explain.
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
Let X = (3) The solution to the system c = 4x + y, y -x + 2y is A. ct) e3t х b+ + 0 where b and care arbitrary constants 3t e -b B. X + C+ 0 where b and care arbitrary constants c. X = ((**)+(11) + (11)e+(1) (1 ).) et est where b and care arbitrary constants -b D. X + c+ 0 where b and care arbitrary constants