Please answer all three parts. (i) Take the laplace transform with respect to t (ii) Solve...
Please answer the blamnks. Thank you. (1 point) Use the Laplace transform to solve the following initial value problem: y6y9y 0,with y(0) 1, y (0) = -4 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation =0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, A Y(s) (s+a} s+a Y(s) Now by inverting the transform,...
Please help solving all parts to this problem and show steps. (1 point) Use the Laplace transform to solve the following initial value problem: x' = 5x + 3y, y = -2x +36 x(0) = 0, y0) = 0 Let X(s) = L{x(t)}, and Ys) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for YS) and X (s): X(S) = Y(s) = Find the partial fraction decomposition of X(s) and...
STRUGGLING PLEASE HELP (1 point) Use the Laplace transform to solve the following initial value problem: y" – 2y + 10y = 0 y(0) = 0, y' (O) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = By completing the square in the denominator and inverting the transform, find yt) =
(3 points) Use Laplace transforms to solve the integral equation y(t) -3 / sin(3v)y(t - v) dv - sin(t) The first step is to apply the Laplace transform and solve for Y(s) = L()(1) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t) =
(6 points) Use the Laplace transform to solve the following initial value problem: y" – 10y' + 40y = 0 y(0) = 4, y'(0) = -5 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) By completing the square in the denominator and inverting the transform, find y(t) =
USE DEFINITION 1 TO DETERMINE THE LAPLACE TRANSFORM OF THE FOLLOWING FUNCTION. f(t)= e sin(t) Laplace Transform Definition 1. Let f(t)be a function on [0,00). The Laplace transform of f is the function defined by the integral The domain of F(s) is all the values of " for which the integral in (1) exists.' The Laplace transform of fis denoted by both and ${/}. QUESTION 2. (3PTS) USE TABLE 7.1 AND 7.2 TO DETERMINE THE LAPLACE TRANSFORM OF THE GIVEN...
(1 point) Use the Laplace transform to solve the following initial value problem: y" + 6y' - 16y = 0 y(0) = 3, y(0) = 1 First, using Y for the Laplace transform of y(t), i.e., Y = C{y(t)). find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(S) = Y(s) = A. where a <b Now by...
(1 pt) Use the Laplace transform to solve the following initial value problem: y" +-6y' + 9y = 0 y0) = 2, y'(0) = 1 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(s) = sta + Y(s) = 2 Now by inverting the...
please solve this with clear answer and details Find the Laplace transform of the following signals and in each case determine the corresponding region of convergence: 3.4 (a) (b) the signal x(t)=e-ulu(t)-eatu-t)when (i) α > 0, (ii) α→0, a sampled signal Xi (t) = e (t n) CHAPTER 3: The Laplace Transform (c) the "stairs to heaven" signal (d) the sinusoidal signal r(t) [cos(2(1-1)) + sin(2π1)]a(1-1), (e) the signal y(t)=t2e-21 u(t) using that x(t)=tathasx(s)=2/s. Answers: (a) As α → 0,x(t)...
(6 points) Use the Laplace transform to solve the following initial value problem: y" + 3y' = 0 y(0) = -3, y'(0) = 6 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 = = + Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) where a <b Y(S) B s+b sta + Now...