This is a differential equation problem
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This is a differential equation problem
4. (10 Points) Use operational properties of the Laplace Transform...
Differential equations 7.4 Operational properties II Formula to use Use operational properties of the Laplace Transform...
Differential equations 7.4 Operational properties II
Formula to use
Use operational properties of the Laplace Transform to determine L{f(x)}, where f(x) is represented in the graph below. Simplify your answer. f(t) 4 1 1 2 3 4 THEOREM 7.4.3 Transform of a Periodic Function If f(t) is piecewise continuous on [0, 0), of exponential order, and periodic with period T, then 1 L{f(t)} es f(t) dt. () di. 1 - e-ST
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y...
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y + 5y = 0 y(0) = 0, y'(0) = 8 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 = 01 Now solve for Y(3) By completing the square in the denominator and inverting the transform, find g(t) =
(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) =
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" +...
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1
*(1-6) (10 points each) Solve each differential equation. (Don't use the Laplace transform). 4. xy -...
*(1-6) (10 points each) Solve each differential equation. (Don't use the Laplace transform). 4. xy - y - xy = 0. It is a Bernoulli equation.
9. (-/10 Points] DETAILS ZILLDIFFEQMODAP11 7.4.045. Use the Laplace transform to solve the given integral equation....
9. (-/10 Points] DETAILS ZILLDIFFEQMODAP11 7.4.045. Use the Laplace transform to solve the given integral equation. f(t) dt = 10 f(t) = 10. [-/10 Points) DETAILS ZILLDIFFEQMODAP11 7.4.056. Use Theorem 7.4.3 to find the Laplace transform F(s) of the given periodic function. f01 1 2 3 4 triangular wave F(s)
Differential equations 7.3 Operational properties I Table for reference if needed. Use operational properties of the...
Differential equations 7.3 Operational properties I
Table for reference if needed.
Use operational properties of the Laplace Transform to show Hint: F(t)=1.5(1) t S+1 t TABLE OF LAPLACE TRANSFORMS f(0) L{f(0) = F(s) f(t) L {f(0)} = F(s) 1. 1 20. eat sinh kt k (s – a) - R2 S 1 s- a 2. t 21. ear cosh kt 52 (s - a)- K 3. " n! +10 n a positive integer 22. tsin kt 2ks (52 + 2)2...
(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...
Problem 3 (5 Points) Using the Laplace transform properties and starting from the Laplace transform of...
Problem 3 (5 Points) Using the Laplace transform properties and starting from the Laplace transform of u(t) find the Laplace transform of te-atu(t) +58"(t)
do problem 2 and 4 Problem #2 Find the Laplace Transform 5t 2 3 Place Transform...
do problem 2 and 4
Problem #2 Find the Laplace Transform 5t 2 3 Place Transform of X(t) = te-* cos(2t +30°) Problem #3 Find the Inverse Laplace Tran Tse Laplace Transform of: s+2 F(S) = (y2 +28+2)(s +1) Problem #4 Find the Inverse Laplace Transform 1-03 (s +2)(1 - e-*) F(s) = Problem #5 For F(s) given in Problem #3 find f(0) and f(co). Problem #6 Use Laplace Transform to find x(t) in the following integra differential equation: dx...
Differential equations 7.4 Operational properties II
Formula to use
Use operational properties of the Laplace Transform to determine L{f(x)}, where f(x) is represented in the graph below. Simplify your answer. f(t) 4 1 1 2 3 4 THEOREM 7.4.3 Transform of a Periodic Function If f(t) is piecewise continuous on [0, 0), of exponential order, and periodic with period T, then 1 L{f(t)} es f(t) dt. () di. 1 - e-ST
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y + 5y = 0 y(0) = 0, y'(0) = 8 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 = 01 Now solve for Y(3) By completing the square in the denominator and inverting the transform, find g(t) =
(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) =
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1
*(1-6) (10 points each) Solve each differential equation. (Don't use the Laplace transform). 4. xy - y - xy = 0. It is a Bernoulli equation.
9. (-/10 Points] DETAILS ZILLDIFFEQMODAP11 7.4.045. Use the Laplace transform to solve the given integral equation. f(t) dt = 10 f(t) = 10. [-/10 Points) DETAILS ZILLDIFFEQMODAP11 7.4.056. Use Theorem 7.4.3 to find the Laplace transform F(s) of the given periodic function. f01 1 2 3 4 triangular wave F(s)
Differential equations 7.3 Operational properties I
Table for reference if needed.
Use operational properties of the Laplace Transform to show Hint: F(t)=1.5(1) t S+1 t TABLE OF LAPLACE TRANSFORMS f(0) L{f(0) = F(s) f(t) L {f(0)} = F(s) 1. 1 20. eat sinh kt k (s – a) - R2 S 1 s- a 2. t 21. ear cosh kt 52 (s - a)- K 3. " n! +10 n a positive integer 22. tsin kt 2ks (52 + 2)2...
(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...
Problem 3 (5 Points) Using the Laplace transform properties and starting from the Laplace transform of u(t) find the Laplace transform of te-atu(t) +58"(t)
do problem 2 and 4
Problem #2 Find the Laplace Transform 5t 2 3 Place Transform of X(t) = te-* cos(2t +30°) Problem #3 Find the Inverse Laplace Tran Tse Laplace Transform of: s+2 F(S) = (y2 +28+2)(s +1) Problem #4 Find the Inverse Laplace Transform 1-03 (s +2)(1 - e-*) F(s) = Problem #5 For F(s) given in Problem #3 find f(0) and f(co). Problem #6 Use Laplace Transform to find x(t) in the following integra differential equation: dx...
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