differential equation Convert the IVP into an IVP for a system in normal ( canonical) form:...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 + 4y = u(t) dt dt where y(t) is the output of the system and u(t) is the input. This is an Initial Value Problem (IVP) with initial conditions y(0) = 0, y = 0. Also by setting u(t) = (t) an input 8(t) is given to the system, where 8(t) is the unit impulse function. a. Write a function F(s) for a function f(t)...
(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) =
The following IVP will be used for Question 1 and Question 2 on this quiz. Solve the initial value problem using the method of Laplace Transforms. y' - y' = 6x y(0) = 2,y'(0) = -1 The solution will be accomplished through answering the two questions below. In using the Laplace Transform to solve the above IVP, solving for Y(s) gives Y(8) = Y(s) = + 8+3 $-2 s-2 Y(s) – + 5 $+2 8-3 3 5 Y(s) = +...
Convert the following Boolean equation to canonical sum-of-minterms form: F(a,b,c) = b'c' Convert the following Boolean equation to canonical sum-of-minterms form: F(a,b,c) = abc' + a'c
Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
Please answer parts c-d only. 4. In lab 4 we consider the differential equation y" 2yywyF(t) for different forcing terms F(t). In this problem we analyze this equation further using Laplace transforms 0, t<1 (a) Consider y" + y, +40y-1(t), where I(t)- t < 2. Find 1 1, 0. t>2 the forward transform Y-E(y) if y(0)-y(0)-0 (b) Solve y" + y, + 40y-1, y(0) = y'(0) = 0, using Laplace transforms Notice how the value of Y (s) you obtain...
Solve the system of equations with Laplace Transforms: (differential equations) all parts please Solve the system of equations with Laplace Transforms: x' + y' = 1, x(0) = y(0) = x'(0) = y'(0) = 0. y" = x' Let X(s) = LT of x(t) and Y(s) = LT of y(1). First obtain expressions for X(s) and Y(s) and list them in the form ready for obtaining their inverses. a. Y(s) = X(s) = %3D b. Now obtain the inverse transforms....
Solve the given integral equation or integro-differential equation for y(t). yʻce) + f(t-v1yv) dv = 4t, y(0)=0 y(t)
Solve the given integral equation or integro-differential equation for y(t). t y (t) + (t - vy(v) dv = 8t, y(O) = 0 0 y(t) =