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Transform the given initial value problem into an equivalent problem with the initial point at the...
Tutorial Exercise Use the Laplace transform to solve the given initial-value problem. y' + 5y =...
Tutorial Exercise Use the Laplace transform to solve the given initial-value problem. y' + 5y = et (0) = 2 Step 1 To use the Laplace transform to solve the given initial value problem, we first take the transform of each member of the differential equation + 6y et The strategy is that the new equation can be solved for ty) algebraically. Once solved, transforming back to an equation for gives the solution we need to the original differential equation....
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand...
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Y(sA2-10s+29)+3s-24 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 -9(s-5(S-5)A2+9) Your answer should be a function of s only. Next equate your last two answers and solve...
Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem:...
Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem: 1, y' + 9 = 0<t<T 0,7 <t< y(0) = 5, y'(0) = 4
(1 point) Consider the initial value problem d'y dy dt2 dt dt Write down the Laplace transform of the left-hand sid...
(1 point) Consider the initial value problem d'y dy dt2 dt dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions 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 Your answer should be a function of s only. Next equate your last two answers and solve for Y. You...
Solve initial value problem using Laplace transform Problem 4 Solve the initial value problems given below...
Solve initial value problem using Laplace transform
Problem 4 Solve the initial value problems given below --ез, y(0) 2. a. b. f ty 3 cos t, y(0)-
(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
(1 point) Take the Laplace transform of the following initial value problem and solve for Y(8)...
(1 point) Take the Laplace transform of the following initial value problem and solve for Y(8) = L{y(t)}; ſ1, 0<t<1 y" – 6y' - 27y= { O, 1<t y(0) = 0, y'(0) = 0 Y(8) = (1-e^(-s)(s(s^2-6s-27)) Now find the inverse transform: y(t) = (Notation: write uſt-c) for the Heaviside step function uct) with step at t = c.) Note: 1 | 1 s(8 – 9)(8 + 3) 36 6 10 + s $+37108 8-9
Find the Laplace transform Y(s) Ay) of the solution of the given initial value problem. A...
Find the Laplace transform Y(s) Ay) of the solution of the given initial value problem. A method of determining the Problems 21 through 24 in Section 6.1. Y"+9 = {1, isted y(0) = 8, y(0) = 3 Y(s) =
ZILLDIFFEQMODAP11 7.2.037.MI. Use the Laplace transform to solve the given initial-value problem.
ZILLDIFFEQMODAP11 7.2.037.MI. Use the Laplace transform to solve the given initial-value problem. y' + 5y = e3t, y(0) = 2 y(t) = _______
Problem #4 Solve the initial value problem as follows: dy dy +4+ (4 x +y) Then determine the positive number r such that - -4.04. Round-off the value of this positive number x to FOUR figures an...
Problem #4 Solve the initial value problem as follows: dy dy +4+ (4 x +y) Then determine the positive number r such that - -4.04. Round-off the value of this positive number x to FOUR figures and present it below (12 points): your mumerical result for the ae ust be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The substitution used to solve the differential equation is as follows (mark...
Tutorial Exercise Use the Laplace transform to solve the given initial-value problem. y' + 5y = et (0) = 2 Step 1 To use the Laplace transform to solve the given initial value problem, we first take the transform of each member of the differential equation + 6y et The strategy is that the new equation can be solved for ty) algebraically. Once solved, transforming back to an equation for gives the solution we need to the original differential equation....
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Y(sA2-10s+29)+3s-24 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 -9(s-5(S-5)A2+9) Your answer should be a function of s only. Next equate your last two answers and solve...
Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem: 1, y' + 9 = 0<t<T 0,7 <t< y(0) = 5, y'(0) = 4
(1 point) Consider the initial value problem d'y dy dt2 dt dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions 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 Your answer should be a function of s only. Next equate your last two answers and solve for Y. You...
Solve initial value problem using Laplace transform
Problem 4 Solve the initial value problems given below --ез, y(0) 2. a. b. f ty 3 cos t, y(0)-
(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
(1 point) Take the Laplace transform of the following initial value problem and solve for Y(8) = L{y(t)}; ſ1, 0<t<1 y" – 6y' - 27y= { O, 1<t y(0) = 0, y'(0) = 0 Y(8) = (1-e^(-s)(s(s^2-6s-27)) Now find the inverse transform: y(t) = (Notation: write uſt-c) for the Heaviside step function uct) with step at t = c.) Note: 1 | 1 s(8 – 9)(8 + 3) 36 6 10 + s $+37108 8-9
Find the Laplace transform Y(s) Ay) of the solution of the given initial value problem. A method of determining the Problems 21 through 24 in Section 6.1. Y"+9 = {1, isted y(0) = 8, y(0) = 3 Y(s) =
Problem #4 Solve the initial value problem as follows: dy dy +4+ (4 x +y) Then determine the positive number r such that - -4.04. Round-off the value of this positive number x to FOUR figures and present it below (12 points): your mumerical result for the ae ust be written here) Also, you must provide some intermediate results obtained by you while solving the problem above: 1) The substitution used to solve the differential equation is as follows (mark...
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