Describe the behavior of the solution corresponding to the initial value a. (a) 2y' − y = e^t/3 , y(0) = a. (b) 3y' − 2y = e^−πt/2 , y(0) = a
Describe the behavior of the solution corresponding to the initial value a. (a) 2y' − y...
Consider the following. (A computer algebra system is recommended.) 11y' − 2y = e−πt/2, y(0) = a (b) Solve the initial value problem. y(t) = Find the critical value a0 exactly. a0 = (c) Describe the behavior of the solution corresponding to the initial value a0. For a0, the solution is y(t) =
please show all steps , thank you 6. Consider the initial value problem y" + 2y' + 2y = (t – 7); y(0) = 0, y'(0) = 1. a. Find the solution to the initial value problem. (10 points) b. Sketch a plot of the solution for t E (0,37]. (5 points) c. Describe the behavior of the solution. How is this system damped? (5 points)
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
#6 Solve the initial value problem y(0)- 2, y,(0) 1 y"-3y' + 2y-6(t-3);
7. Given the initial-value problem y" + 3y' + 2y = 4x2, y(0) = 3, y'0) = 1, a. Find its homogeneous solution using the Constant Coefficient approach (10pts) b. Find is particular solution using the Annihilator method. (10pts) c. Find the general solution that satisfies the initial conditions. (5pts)
1. Solve the initial value problem =[71]e, 20 = [2] Describe the behavior of the solution as t + 0.
Use Laplace transforms to solve the following initial value problems. Where possible, describe the solution behavior in terms of oscillation and decay. y′′ +4y = δ(t−1), y(0) = 3, y′(0) = 0.
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
use the Laplace transform to solue the initial value problem y - 3y +2y = h (t) Y(o)=0 yo(o)=0 where h(t): 0,0 Lt L4 t> 4 { 2
Solve the initial value problem :-( 17.00 (3) and describe the behavior of the solution as t - 00