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Problem #8: Consider the following integral equation, so called because the unknown dependent variable y appears...
Problem #6: Consider the following integral equation, so called integral because the unknown depe...
Problem #6: Consider the following integral equation, so called integral because the unknown dependent variable y appears within an This equation is defined for t0 (a) Use convolution and Laplace transforms to find the Laplace transform of the solution (b) Obtain the solution y(t) Enter your answer as a symbolic function of s, as in these examples Problem #6(a): Enter your answer as a symbolic function of t, as in these examples Problem #6(b): Just Save Submit Problem #6 for...
Consider the following integral equation, so called because the unknown dependent variable y appears within an...
Consider the following integral equation, so called because the
unknown dependent variable y appears within an
integral:
t
∫
0
sin[5(t − w)] y(w) dw
= 5t2
This equation is defined for t ≥ 0.
(a)
Use convolution and Laplace transforms to find the Laplace
transform of the solution.
(b)
Obtain the solution y(t).
Consider the following integral equation, so called because the unknown dependent variable y appears within an integral: Ś sin sin[5(t – w)] y(w) dw = 5t2...
Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y...
Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y Find Y(s), the Laplace transform ofy() Enter your answer as a symbolic function of s, as in these examples Problem #2: Submit Problem #2 for Grading Just Save Attempt #3 Problem #2 Attempt # 2 Attempt #5 Attempt#1 Attempt #4 Your Answer: Your Mark
(1 point) Let g(t) = e2t. a. Solve the initial value problem y – 2y =...
(1 point) Let g(t) = e2t. a. Solve the initial value problem y – 2y = g(t), y(0) = 0, using the technique of integrating factors. (Do not use Laplace transforms.) y(t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem $' – 20 = 8(t), $(0) = 0. $(t) = c. Evaluate the convolution integral (0 * g)(t) = Só "(t – w) g(w) dw, and compare the resulting function with the...
Problem #16; Use the Laplace transform to solve the following initial value problem y2y35 t-4), y(0)...
Problem #16; Use the Laplace transform to solve the following initial value problem y2y35 t-4), y(0) = 0. y'(0) 0 The solution is of the form Ug(t] h(t). (a) Enter the function g(f) into the answer box below. (b) Enter the function h(t) into the answer box below Enter your answer as a symbolic function of t. as in these Problem #16(a): examples Enter your answer as a symbolic function of t. as in these examples Problem 16(b): Submit Problem...
where h is the Use the Laplace transform to solve the following initial value problem: y"+y...
where h is the Use the Laplace transform to solve the following initial value problem: y"+y + 2y = h(t – 5), y(0) = 2, y(0) = -1, Heaviside function. In the following parts, use h(t – c) for the shifted Heaviside function he(t) when necessary. 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)}. L{y(t)}(s) = b. Express the solution y(t) as the...
(t)= . Use the Laplace transform to solve the following initial value problem: 44" + 2y...
(t)= . Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3+), 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. L{y(t)}(s) b. Express the solution y(t) in terms of a...
Problem #12: The inverse Laplace transform f( = £"{F(s)} of the function ei(-3s +8) F(s) s249...
Problem #12: The inverse Laplace transform f( = £"{F(s)} of the function ei(-3s +8) F(s) s249 is of the form g(i) U[h{f)]. (a) Enter the function g(t) into the answer box below (b) Enter the function A(t) into the answer box below. Enter your answer as a symbolic function of t. as in these examples Problem #12(a): Enter your answer as a symbolic function of t, as in these examples Problem 12(b) Submit Problem #12 for Grading Just Save Problem...
2. Consider the following initial value problem i-6 8 2e-3t. (0)0, (0) = 0. = (a)...
2. Consider the following initial value problem i-6 8 2e-3t. (0)0, (0) = 0. = (a) Using Laplace transforms find the Green's function g(t) of the initial value problem (b) Hence write down the solution to the initial value problem as a convolution integral Do not evaluate the convolution integral
2. Consider the following initial value problem i-6 8 2e-3t. (0)0, (0) = 0. = (a) Using Laplace transforms find the Green's function g(t) of the initial value problem (b)...
Problem #7: Solve the following boundary value problem. y" - 12y + 36y 0, y) =...
Problem #7: Solve the following boundary value problem. y" - 12y + 36y 0, y) = 9, y(1) = 10 Problem #7: Enter your answer as a symbolic function of x, as in these examples Do not include 'y = 'in your answer. Just Save Submit Problem #7 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #7 Your Answer: Your Mark: Problem #8: Solve the following initial value problem. y'"' – 9y" + 24y' –...
Problem #6: Consider the following integral equation, so called integral because the unknown dependent variable y appears within an This equation is defined for t0 (a) Use convolution and Laplace transforms to find the Laplace transform of the solution (b) Obtain the solution y(t) Enter your answer as a symbolic function of s, as in these examples Problem #6(a): Enter your answer as a symbolic function of t, as in these examples Problem #6(b): Just Save Submit Problem #6 for...
Consider the following integral equation, so called because the
unknown dependent variable y appears within an
integral:
t
∫
0
sin[5(t − w)] y(w) dw
= 5t2
This equation is defined for t ≥ 0.
(a)
Use convolution and Laplace transforms to find the Laplace
transform of the solution.
(b)
Obtain the solution y(t).
Consider the following integral equation, so called because the unknown dependent variable y appears within an integral: Ś sin sin[5(t – w)] y(w) dw = 5t2...
Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y Find Y(s), the Laplace transform ofy() Enter your answer as a symbolic function of s, as in these examples Problem #2: Submit Problem #2 for Grading Just Save Attempt #3 Problem #2 Attempt # 2 Attempt #5 Attempt#1 Attempt #4 Your Answer: Your Mark
(1 point) Let g(t) = e2t. a. Solve the initial value problem y – 2y = g(t), y(0) = 0, using the technique of integrating factors. (Do not use Laplace transforms.) y(t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem $' – 20 = 8(t), $(0) = 0. $(t) = c. Evaluate the convolution integral (0 * g)(t) = Só "(t – w) g(w) dw, and compare the resulting function with the...
Problem #16; Use the Laplace transform to solve the following initial value problem y2y35 t-4), y(0) = 0. y'(0) 0 The solution is of the form Ug(t] h(t). (a) Enter the function g(f) into the answer box below. (b) Enter the function h(t) into the answer box below Enter your answer as a symbolic function of t. as in these Problem #16(a): examples Enter your answer as a symbolic function of t. as in these examples Problem 16(b): Submit Problem...
where h is the Use the Laplace transform to solve the following initial value problem: y"+y + 2y = h(t – 5), y(0) = 2, y(0) = -1, Heaviside function. In the following parts, use h(t – c) for the shifted Heaviside function he(t) when necessary. 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)}. L{y(t)}(s) = b. Express the solution y(t) as the...
(t)= . Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3+), 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. L{y(t)}(s) b. Express the solution y(t) in terms of a...
Problem #12: The inverse Laplace transform f( = £"{F(s)} of the function ei(-3s +8) F(s) s249 is of the form g(i) U[h{f)]. (a) Enter the function g(t) into the answer box below (b) Enter the function A(t) into the answer box below. Enter your answer as a symbolic function of t. as in these examples Problem #12(a): Enter your answer as a symbolic function of t, as in these examples Problem 12(b) Submit Problem #12 for Grading Just Save Problem...
2. Consider the following initial value problem i-6 8 2e-3t. (0)0, (0) = 0. = (a) Using Laplace transforms find the Green's function g(t) of the initial value problem (b) Hence write down the solution to the initial value problem as a convolution integral Do not evaluate the convolution integral
2. Consider the following initial value problem i-6 8 2e-3t. (0)0, (0) = 0. = (a) Using Laplace transforms find the Green's function g(t) of the initial value problem (b)...
Problem #7: Solve the following boundary value problem. y" - 12y + 36y 0, y) = 9, y(1) = 10 Problem #7: Enter your answer as a symbolic function of x, as in these examples Do not include 'y = 'in your answer. Just Save Submit Problem #7 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #7 Your Answer: Your Mark: Problem #8: Solve the following initial value problem. y'"' – 9y" + 24y' –...
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