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Problem #6: Consider the following integral equation, so called integral because the unknown depe...
Problem #8: Consider the following integral equation, so called because the unknown dependent variable y appears...
Problem #8: Consider the following integral equation, so called because the unknown dependent variable y appears within an integral sin[4(t- w) y(w) dw = 82 This equation is defined for t z 0. (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 #8(a) Enter your answer as a symbolic function of t, as in these examples...
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
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...
Problem #4: Find the inverse Laplace transform of the following expression 10s 3 2-251 Enter your...
Problem #4: Find the inverse Laplace transform of the following expression 10s 3 2-251 Enter your answer as a symbolic function of t, as in these examples Problem #4 Submit Problem #4 for Grading Just Save Attempt #4 Attempt #5 Attempt #3 Problem #4 Attempt #2 Attempt #1 Your Answer: Your Mark:
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...
Problem #6: Find the Laplace transform of the following functions 4 0<t 3 9 tz3 (a)...
Problem #6: Find the Laplace transform of the following functions 4 0<t 3 9 tz3 (a) f(t) (b) f(t) 9>10 7 0 t2 6 0 t</9 cos[10(/9) tz n/9 f(f = symbolic Enter your answer as a function of s, as in these examples Problem #6(a): symbolic Enter your answer as a function of s, as in these examples Problem #6(b): Enter your answer as a symbolic function of s, as in these examples Problem #6(c):
Problem #6: Find the...
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 #8: A rod of length 9 coincides with the interval [0,9] on the x-axis. Consider...
Problem #8: A rod of length 9 coincides with the interval [0,9] on the x-axis. Consider the heat equation in the special case when k=1 if both ends are held at temperature zero for all t> 0. The initial temperature is f(x) throughout where f(x) = a sin(876x) + b sin(4x) The solution to the heat equation under the above conditions is of the form u (x, t) = a g1(x, t) + b g2(x, t) (a) Enter the function...
Problem #8: Consider the following integral equation, so called because the unknown dependent variable y appears within an integral sin[4(t- w) y(w) dw = 82 This equation is defined for t z 0. (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 #8(a) Enter your answer as a symbolic function of t, as in these examples...
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
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...
Problem #4: Find the inverse Laplace transform of the following expression 10s 3 2-251 Enter your answer as a symbolic function of t, as in these examples Problem #4 Submit Problem #4 for Grading Just Save Attempt #4 Attempt #5 Attempt #3 Problem #4 Attempt #2 Attempt #1 Your Answer: Your Mark:
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...
Problem #6: Find the Laplace transform of the following functions 4 0<t 3 9 tz3 (a) f(t) (b) f(t) 9>10 7 0 t2 6 0 t</9 cos[10(/9) tz n/9 f(f = symbolic Enter your answer as a function of s, as in these examples Problem #6(a): symbolic Enter your answer as a function of s, as in these examples Problem #6(b): Enter your answer as a symbolic function of s, as in these examples Problem #6(c):
Problem #6: Find the...
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' –...
Problem #8: A rod of length 9 coincides with the interval [0,9] on the x-axis. Consider the heat equation in the special case when k=1 if both ends are held at temperature zero for all t> 0. The initial temperature is f(x) throughout where f(x) = a sin(876x) + b sin(4x) The solution to the heat equation under the above conditions is of the form u (x, t) = a g1(x, t) + b g2(x, t) (a) Enter the function...
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