2. i) Find the general solutions without using Laplace transform. a) ° +9y = 2cos(x) b)...
Solve the following initial value problem using the Laplace Transform: y" + 9y = 6 cos(3x) with y(0) = -1 and y'(0) = 1
MATLAB HELP
(a) Use the command dsolve to find general solutions to the
differential equations below. i. y 00 + 3y = 0 ii. y 00 + 4y 0 +
29y = 0 iii. y 00 − y/36 = 0 iv. y 00 + 2y 0 + y = 0 v. y 00 + 6y 0
+ 5y = 0 (b) Graph each of the solutions in (a) in the same window
with 0 ≤ t ≤ 10, using the...
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...
2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a
2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a
Find the solutions in the time domain of the following second-order differential equation using the Laplace transform, (2a) (2b) (24) ii(t) + 39(t)-sin(t); y(0) = 1; (O) = 2.
Consider the following statements.
(i) The Laplace Transform of
11tet2 cos(et2)
is well-defined for some values of s.
(ii) The Laplace Transform is an integral transform that turns
the problem of solving constant coefficient ODEs into an algebraic
problem. This transform is particularly useful when it comes to
studying problems arising in applications where the forcing
function in the ODE is piece-wise continuous but not necessarily
continuous, or when it comes to studying some Volterra equations
and integro-differential equations.
(iii)...
1. Find general solutions to the following differential systems of equations using dsolve: a. x' = y + t, y' = 2 -x+t b. x'=s-X, y' = -y - 3x, C. X" = x - x - y, y = -x- y - y - s', s" = -95 d. Solve the equations in c. above with the initial conditions x(0) = 1, x'(0) = 0, y(0) = -1, y'(0) = 0, $(0) = 1, s'(0) = 0, and plot...
could someone explain this with helpful workspace?
Problem 3. (1 point) Use the Laplace transform to solve the following initial value problem: y" +9y' = 0 y(0) = 3, y(0) = 5 a. 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 b. Now solve for Y(S) = c. Write the above answer in its partial fraction decomposition, Y(s) = sta +...
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...
x'-y,y 10x-7y using the method of elimination. 2) a) Find the general solution to b) What happens to all solutions as ? You should find that all solutions approach the same point (x, y). This is an example of a fixed point. c) Find the particular solution to the IVP consisting of the above system of equations and the conditions x(0)2, y(0)-7