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5. Consider the following initial value problems: x" + 16x...
Homework 16: Problem 3 Previous Problem Problem List Next Problem (1 point) Consider the initial value...
Homework 16: Problem 3 Previous Problem Problem List Next Problem (1 point) Consider the initial value problem y" + 16y = 64t, y(0) = 9, y'(0) = 6. 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). help (formulas) b. Solve...
STRUGGLING PLEASE HELP (1 point) Use the Laplace transform to solve the following initial value problem:...
STRUGGLING PLEASE HELP
(1 point) Use the Laplace transform to solve the following initial value problem: y" – 2y + 10y = 0 y(0) = 0, y' (O) = 3 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 = 0 Now solve for Y(s) = By completing the square in the denominator and inverting the transform, find yt) =
(1 point) Use the Laplace transform to solve the following initial value problem: y" + 6y'...
(1 point) Use the Laplace transform to solve the following initial value problem: y" + 6y' - 16y = 0 y(0) = 3, y(0) = 1 First, using Y for the Laplace transform of y(t), i.e., Y = C{y(t)). find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(S) = Y(s) = A. where a <b Now by...
STRUGGLING WITH THIS ONE PLEASE HELP ME (1 point) Consider the initial value problem y" +...
STRUGGLING WITH THIS ONE PLEASE HELP ME
(1 point) Consider the initial value problem y" + 16 = 32t, y(O) = 4, y(0) = 3. 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). = help (formulas) b. Solve your equation...
(1 point) Use the Laplace transform to solve the following initial value problem: y! -8y +...
(1 point) Use the Laplace transform to solve the following initial value problem: y! -8y + 20y = 0 y(O) = 0, y (0) = 2 First, using Y for the Laplace transform of y(t), i.e., Y = {y(0), find the equation you get by taking the Laplace transform of the differential equation 2/(s(2)-8s+20) =0 Now solve for Y(s) = 1/[(9-4) (2)+(2)^(2)) By completing the square in the denominator and inverting the transform, find y() = (4t)sint
(5 points) Consider the following initial value problem: Y" - 2y - 35y = sin(4t) y(0)...
(5 points) Consider the following initial value problem: Y" - 2y - 35y = sin(4t) y(0) = 3, y'(0) = -4 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) = (35+2)/(s^2-25-35)+4/((s^2-28-35)*(s^2+16))
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation...
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation y" (t) + 16y'(t) + 68y(t) = –20e-4t u(t), with initial conditions y(0) = -3, and y'(0) = 4. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the...
(6 points) Use the Laplace transform to solve the following initial value problem: y" – 10y'...
(6 points) Use the Laplace transform to solve the following initial value problem: y" – 10y' + 40y = 0 y(0) = 4, y'(0) = -5 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 = 0 Now solve for Y(s) By completing the square in the denominator and inverting the transform, find y(t) =
having trouble finding y(t) NOT Correct (1 point) Consider the initial value problem y"+16y 48t, y(0)3,...
having trouble finding y(t)
NOT Correct (1 point) Consider the initial value problem y"+16y 48t, y(0)3, /(0)-9. 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). (s 2Y(s)-3s-9)+16Y(s) help (formulas) 48/s 2 b. Solve your equation for Y(s). C{y(t))=48/(s 2(s2+ 16)...
(6 points) Use the Laplace transform to solve the following initial value problem: y" + 3y'...
(6 points) Use the Laplace transform to solve the following initial value problem: y" + 3y' = 0 y(0) = -3, y'(0) = 6 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 = 0 = = + Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) where a <b Y(S) B s+b sta + Now...
Homework 16: Problem 3 Previous Problem Problem List Next Problem (1 point) Consider the initial value problem y" + 16y = 64t, y(0) = 9, y'(0) = 6. 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). help (formulas) b. Solve...
STRUGGLING PLEASE HELP
(1 point) Use the Laplace transform to solve the following initial value problem: y" – 2y + 10y = 0 y(0) = 0, y' (O) = 3 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 = 0 Now solve for Y(s) = By completing the square in the denominator and inverting the transform, find yt) =
(1 point) Use the Laplace transform to solve the following initial value problem: y" + 6y' - 16y = 0 y(0) = 3, y(0) = 1 First, using Y for the Laplace transform of y(t), i.e., Y = C{y(t)). find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(S) = Y(s) = A. where a <b Now by...
STRUGGLING WITH THIS ONE PLEASE HELP ME
(1 point) Consider the initial value problem y" + 16 = 32t, y(O) = 4, y(0) = 3. 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). = help (formulas) b. Solve your equation...
(1 point) Use the Laplace transform to solve the following initial value problem: y! -8y + 20y = 0 y(O) = 0, y (0) = 2 First, using Y for the Laplace transform of y(t), i.e., Y = {y(0), find the equation you get by taking the Laplace transform of the differential equation 2/(s(2)-8s+20) =0 Now solve for Y(s) = 1/[(9-4) (2)+(2)^(2)) By completing the square in the denominator and inverting the transform, find y() = (4t)sint
(5 points) Consider the following initial value problem: Y" - 2y - 35y = sin(4t) y(0) = 3, y'(0) = -4 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) = (35+2)/(s^2-25-35)+4/((s^2-28-35)*(s^2+16))
(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation y" (t) + 16y'(t) + 68y(t) = –20e-4t u(t), with initial conditions y(0) = -3, and y'(0) = 4. Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the...
(6 points) Use the Laplace transform to solve the following initial value problem: y" – 10y' + 40y = 0 y(0) = 4, y'(0) = -5 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 = 0 Now solve for Y(s) By completing the square in the denominator and inverting the transform, find y(t) =
having trouble finding y(t)
NOT Correct (1 point) Consider the initial value problem y"+16y 48t, y(0)3, /(0)-9. 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). (s 2Y(s)-3s-9)+16Y(s) help (formulas) 48/s 2 b. Solve your equation for Y(s). C{y(t))=48/(s 2(s2+ 16)...
(6 points) Use the Laplace transform to solve the following initial value problem: y" + 3y' = 0 y(0) = -3, y'(0) = 6 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 = 0 = = + Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) where a <b Y(S) B s+b sta + Now...
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