Problem 9 6.3, Exercise 7. Solve the initial value problem where r(0)-1 and y(0)-2
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where 8(t-1) is Dirac's delta function and S4 if 0<t<1 r(t) 8 if t > 1 (a) Represent r(t) using unit step functions. (b) Find the Laplace Transform of 8(t-1)+r(t). (c) Solve the above initial value problem. {
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
2. Solve the initial value problem = 4x + 2y, = 2x + y with r(0) = 1, y(0) = 0.
Solve the initial value problem. 7 dy + 9y - 9 e-X = 0, y(0) = dx 8 The solution is y(x) =
Question 9 In Exercises 7–11 solve the initial value problem. 7. y' – 2y = xy3, y(0) = 2/2 8. y' – xy = xy3/2, y(1) = 4 9. xy' + y = x4y4, y(1) = 1/2 10. y' – 2y = 2y1/2, y(0) = 1 11. y' – 4y = 402, y(0) = 1
Solve the given initial-value problem. - 5y = 0, y(1) = 0, y'(1) = 9 OL
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184' +81y = 4472; y(0) = -3, v'(0) = -2. (1) Let C and Cybe arbitrary constants. The general solution to the related homogeneous differential equation y" – 18y' +81y = 0 is the function yh() = C1 yı() + C2 y2() = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(T) + C29(2) #C19() +C2f(). is of...
Solve the initial value problem: 4y" +12y + 17y= 0, y(1/2) = 1, y(7/2) = 1. Give your answer as y=... . Use x as the independent variable. Answer:
9. Solve the initial value problem using the Laplace transform y" + 3y = f(t), y(0) = 0, y(0) = 1, where f(t) = { ( 1 home s 2, if 0 <t<5 1, if t > 5 (6
7. Solve the initial value problem --( y = -1 00 when the initial value is given as following: and discuss the behavior of the solution as t (you may sketch the solution curve.) (a) X(0) = (0,0.5). 7. Solve the initial value problem --( y = -1 00 when the initial value is given as following: and discuss the behavior of the solution as t (you may sketch the solution curve.) (a) X(0) = (0,0.5).