Determine the Laplace transform (Y(s)) for the differential equation below: 2y () + Зу() — 32,...
QUESTION 1 Determine the Laplace transform (Y(s) ) for the differential equation below: y"(t)2y'(t)3y(t) 32, y(0) = 15, y'(0) 1, y"(0) = 0 Y(s) = (15*s^1 + 63) (SA3S^2 2s + 3) Y(s) (15sA2 + 31 s^1 + 32) /(sA3 + s^2 + 3s + 0) Y(s) (s^2 6*s^1 15) / (s^2 2s 3) 63) / (s^2 2s Y(s) (15*s^1 3) +
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1
Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3t), y(0) = 0, y(0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. 3s L{y(t)}(s) = (452 + 25 +2s + 18)(52+9) b. Express the...
3. Using Laplace transform, solve the differential equation y" +2y' +y=te* given that y(0) = 1, y'(0)= -2.
Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the differential equation. Recall: h(t - a) is the unit step function shifted to the right a units. y" + 25y = (4t – 8)h(t – 2) - (4t – 12)h(t – 3), y(0) = y' (O) = 0 Y(S) =
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2
Apply the Laplace transform to the differential equation, and solve for Y(s). DO NOT solve the differential equation. Recall: h(t - a) is the unit step function shifted to the right a units. y" + 25y = (3t - 6)h(t – 2) - (3t – 12)h(t – 4), y(0) = y' (O) = 0 Y(8) -
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Laplace transform of the left-hand side of the equation given the initial conditions (sA2-8s+41)Y+2s-18 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation (-8s+32)/(sA2-8s+20) Your answer should be a function of s only...
Determine the inverse Laplace transform of the function below. Se - 2s S2 + 8s +32 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. - 2s Se - 1 >(t) = $2 +85 +32 (Use parentheses to clearly denote the argument of each function.)
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y + 5y = 0 y(0) = 0, y'(0) = 8 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 = 01 Now solve for Y(3) By completing the square in the denominator and inverting the transform, find g(t) =