use Laplace transform dx+2 dx + x = 5e»?' +1 And the initial conditions are, x(0)=2...
Solve using Laplace transform: y"-4y'=5e^x, y(0)=0, y'(0)=1
9. Use the Laplace transform to solve the system dx -xty dt dy dt x(0) = 0, y(0) = 1 = 2x
7. Use the Laplace transform to solve the system dx dt -x + y dy = 2x dt x(0) = 0, y(0) = 1
1. [5 pts] Unilateral Laplace Transform. Use the unilateral Laplace transform to determine the response of the system described by the following differential equation with the given inputs and initial conditions:LaTeX: \frac{\rm d}{ {\rm d} t } y(t) + \ 10y(t) = \ 10x(t), d d t y ( t ) + 10 y ( t ) = 10 x ( t ) , LaTeX: y(0^-) = 1, x(t) u(t) = u(t). y ( 0 − ) = 1 ,...
Use the Laplace transform to solve initial value problems
3. tx" + 2(t-1)x' - 2x = 2, x(0) = 0.
Use the Laplace transform to solve initial value problems
2. x" + 6x' + 18x sin 2t, x(0) = -1, x'0) = 1.
Sheet1 Control 1. Solve the following differential equations using Laplace transforms. Assume zero initial conditions dx + 7x = 5 cos 21 di b. + 6 + 8x = 5 sin 31 dt + 25x = 10u(1) 2. Solve the following differential equations using Laplace transforms and the given initial conditions: de *(0) = 2 () = -3 dx +2+2x = sin21 di dx di dx di 7+2 x(0) = 2:0) = 1 ed + 4x x(0) = 1:0) =...
use the Laplace transform to solve the given system of differential equations dx dt dx dt dt dt x(0) 0, y(o)0 x(t) =
(1 point) Use the Laplace transform to solve the following initial value problem: "7-0 (0)7, (0)-2 First, using Y for the Laplace transform of ), .e.Y Cu)). find the equation you get by taking the Laplace transform of the differential equation Now solve for Y(s) and write the above answer in its partial fraction decomposition, y(s)-- + where a < b Now by inverting the transform, find y(t)
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...