Consider the equation (D2 + 2D + 2)y = cos(t). Which of the following is a...
QUESTION 1 To find a particular solution of the differential equation (D - 1)?(D – 2)(D2 + 1)y = e* + cos – 2 sin z one can use the following trial solution OA Ao + A, cos x + A2 sin OB Anx?et + x² (A, COS I+ A2 sin I) Ос. Aoxe" + x(A, COS X + A2 sin x) OD. Age* + x(A, COS I+ A2 sin x) OC Apx?et + ](A, COS I + A2 sin...
can someone solve this differential equation. I'll definitely leave good remarks The particular integral of (D2 – 2D + 4)y = ex cos x of Select one: 1 że*(3cosx + sinx) a. 10eX3cosx + sinx) O b. 1 क ex COS X 2 C. -1 e*(3cosx - sinx) 10 0 d.
Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y) 40e 2e) cos(8t)+5 eu 2t) sin(8t)/ - 12e - 0. 8 sin(4y) y a. (4/20) Just by reordering terms on the left hand side above, write the equation as Ny + M 0 for appropriate functions N, M. Then compute: aN(t, y) ayM(t, y) b. (8/20) Find an integrating factor If you keep an integrating constant, call it c (t) N and M M,...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are constant, for all t20 (the equilibrium solutions). b) In what regions are solutions increasing? Decreasing? c) Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing? d) Sketch the direction field and verify that it is consistent with parts a through c. a) The solutions are constant for (Type an equation. Use a comma to separate answers as needed.)...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are constant, for all t20 (the equilibrium solutions). b) In what regions are solutions increasing? Decreasing? c) Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing? d) Sketch the direction field and verify that it is consistent with parts a through c. a) The solutions are constant for (Type an equation. Use a comma to separate answers as needed.)...
Consider the differential equation y' (t) = (y-4)(1 + y). a) Find the solutions that are constant, for all t2 0 (the equilibrium solutions). b) In what regions are solutions increasing? Decreasing? c) Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing? d) Sketch the direction field and verify that it is consistent with parts a through c. a) The solutions are constant for (Type an equation. Use a comma to separate answers as...
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
differential equations A particular solution of the equation y" + 16 y = 241 + 2 sin(4 t) should have the form: ae4l+ct sin(4 t) +et cos(4t) ett + c sin(4 t) + e cos(4 t) a e^tt+ ct sin(4 t) a e"! + c sin(4t)
Consider the following integral equation, so called because the unknown dependent variable y appears within an integral: t ∫ 0 sin[5(t − w)] y(w) dw = 5t2 This equation is defined for t ≥ 0. (a) Use convolution and Laplace transforms to find the Laplace transform of the solution. (b) Obtain the solution y(t). Consider the following integral equation, so called because the unknown dependent variable y appears within an integral: Ś sin sin[5(t – w)] y(w) dw = 5t2...
Consider the following differential equation for A = 4 and B = 4: y''(t) + Ay'(t) + By(t) = 1u(t) + -1t u(t) where u(t) is the unit step function. Assume initial conditions: y'(0) = -4 y(0) = 2 Solve this differential equation to obtain an answer of the form shown below. Enter the value for the coefficient c3. Please enter your answer as a number in decimal format (not a fraction). y(t) = co0(t) + Ga(t) + c2 ta(t)...