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Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) =...
y" – 7y' +12 y = 0, y(0) = 3, y'(0) = -2. a. (4/10) Find...
y" – 7y' +12 y = 0, y(0) = 3, y'(0) = -2. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, y" + 10 y' + 25 y=0, y(0) = 5, y (0) = -5. a. (4/10) Find the Laplace Transform of the solution, Y(s) = L[y(t)]. Y(s) =...
Consider the initial value problem for function y given by, Consider the initial value problem for...
Consider the initial value problem for function y given by,
Consider the initial value problem for function y given by, (a) Find the Laplace Transform of the source function, F(s) = L[-3 F(s) = (b) Find the Laplace Transform of the solution, Y(s) Lt) Y(s) - (c) Find the solution y(t) of the initial value problem above. s(t) Recall: If needed, the step function at c is denoted as u(t - c) -1] Help Entering Answers Preview My Anawers Submit...
Consider the following initial value problem. y′ + 5y = { 0 t ≤ 1 10...
Consider the following initial value problem.
y′ + 5y =
{
0
t ≤ 1
10
1 ≤ t < 6
0
6 ≤ t < ∞
y(0) = 4
(a)
Find the Laplace transform of the right hand side of the above
differential equation.
(b)
Let y(t) denote the solution to the above
differential equation, and let Y((s) denote the
Laplace transform of y(t). Find
Y(s).
(c)
By taking the inverse Laplace transform of your answer to (b),
the...
(2 points) Consider the initial value problem y' +8y +41y = g(t), y(0) = 0, y(0)...
(2 points) Consider the initial value problem y' +8y +41y = g(t), y(0) = 0, y(0) = 0, where g(t) = if 9 t<oo. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y() by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below) ! help (formulas) b. Solve your equation for...
Consider the following initial value problem. y" + 6y' + 34y = 8( - 1T) +...
Consider the following initial value problem. y" + 6y' + 34y = 8( - 1T) + 6(t – 7), 7(0) = 1, y(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) Use the Laplace transform to solve the given initial-value problem. y(t) = ])-( * sin(70) .).2(e-) + ( [ - alt- Need Help? Read it Talk to a Tutor
(1 point) Consider the initial value problem y" + 4y = 8t, y(0) =3, y'(0) =...
(1 point) Consider the initial value problem y" + 4y = 8t, y(0) =3, y'(0) = 4. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 8/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = c. Take...
Part B (5 points each] An initial value problem y' + 2y = f(©),y(0) = 0...
Part B (5 points each] An initial value problem y' + 2y = f(©),y(0) = 0 is to be solved by Laplace transforms. (B-1) When f(t) is depicted in the following, show that its Laplace transform can be obtained as f(t) 4 4e F(s) = [[f(t)) = 5ż (1-es). 4 -S s V 2 0 1 2: (B-2) Show that the Laplace transform of the solution, Y(s) = Ly(0)], can be obtained as 4 4(+ 1) Y(s) = s-(s +...
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where...
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where 8(t-1) is Dirac's delta function and S4 if 0<t<1 r(t) 8 if t > 1 (a) Represent r(t) using unit step functions. (b) Find the Laplace Transform of 8(t-1)+r(t). (c) Solve the above initial value problem. {
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has bee...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0)...
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 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 and solve for Y(s)
y" – 7y' +12 y = 0, y(0) = 3, y'(0) = -2. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, y" + 10 y' + 25 y=0, y(0) = 5, y (0) = -5. a. (4/10) Find the Laplace Transform of the solution, Y(s) = L[y(t)]. Y(s) =...
Consider the initial value problem for function y given by,
Consider the initial value problem for function y given by, (a) Find the Laplace Transform of the source function, F(s) = L[-3 F(s) = (b) Find the Laplace Transform of the solution, Y(s) Lt) Y(s) - (c) Find the solution y(t) of the initial value problem above. s(t) Recall: If needed, the step function at c is denoted as u(t - c) -1] Help Entering Answers Preview My Anawers Submit...
Consider the following initial value problem.
y′ + 5y =
{
0
t ≤ 1
10
1 ≤ t < 6
0
6 ≤ t < ∞
y(0) = 4
(a)
Find the Laplace transform of the right hand side of the above
differential equation.
(b)
Let y(t) denote the solution to the above
differential equation, and let Y((s) denote the
Laplace transform of y(t). Find
Y(s).
(c)
By taking the inverse Laplace transform of your answer to (b),
the...
(2 points) Consider the initial value problem y' +8y +41y = g(t), y(0) = 0, y(0) = 0, where g(t) = if 9 t<oo. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y() by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below) ! help (formulas) b. Solve your equation for...
Consider the following initial value problem. y" + 6y' + 34y = 8( - 1T) + 6(t – 7), 7(0) = 1, y(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) Use the Laplace transform to solve the given initial-value problem. y(t) = ])-( * sin(70) .).2(e-) + ( [ - alt- Need Help? Read it Talk to a Tutor
(1 point) Consider the initial value problem y" + 4y = 8t, y(0) =3, y'(0) = 4. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 8/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = c. Take...
Part B (5 points each] An initial value problem y' + 2y = f(©),y(0) = 0 is to be solved by Laplace transforms. (B-1) When f(t) is depicted in the following, show that its Laplace transform can be obtained as f(t) 4 4e F(s) = [[f(t)) = 5ż (1-es). 4 -S s V 2 0 1 2: (B-2) Show that the Laplace transform of the solution, Y(s) = Ly(0)], can be obtained as 4 4(+ 1) Y(s) = s-(s +...
Consider the initial value problem y" +3y' +2y = (t-1)+r(t), y(0) = y(0) = 0, where 8(t-1) is Dirac's delta function and S4 if 0<t<1 r(t) 8 if t > 1 (a) Represent r(t) using unit step functions. (b) Find the Laplace Transform of 8(t-1)+r(t). (c) Solve the above initial value problem. {
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 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 and solve for Y(s)
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