Differential equations 7.3 Operational properties I
Table for reference if needed.
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Differential equations 7.3 Operational properties I
Table for reference if needed.
Use operational properties of the...
Differential equations 7.2 Inverse transforms and transforms of derivatives Use Laplace Transforms to solve the initial...
Differential equations 7.2 Inverse transforms and transforms of
derivatives
Use Laplace Transforms to solve the initial value problem y" + 4y = 25xe", y(0)=-2, and y'(0)=1. 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 +...
Differential equations 7.2 Inverse transforms and transforms of derivatives Use Laplace Transforms to solve the initial...
Differential equations 7.2 Inverse transforms and transforms of
derivatives
Use Laplace Transforms to solve the initial value problem y" – 2y'+5y=-25x , y(0)=2, and y'(0)=3. 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...
III. When solving this problem show all the steps needed to transform the expressions into ones...
III. When solving this problem show all the steps needed to transform the expressions into ones that can be (10) found in the table and indicate the entry of the table used in each step. a) Find the Laplace transform F(s) of the function (5+234 +5e-2) cos(6t) b) Find the inverse Laplace transform f(t) of the function F(s) = 2 s2 + 2s + 5 f(t)=L-'{F(s) Table of Laplace Transforms F(s)=L{()} f(t)= L-'{F(s) F(s)=L{f(t)} 1. 2. et s-a 3. r",...
Page 2 II. (7) Use the Laplace transform to solve the IVP y" - 5y' +...
Page 2 II. (7) Use the Laplace transform to solve the IVP y" - 5y' + 6y = 8(t-1), y(0) = 0,0) = 0, where the right hand side is the Dirac Delta Function (t - to) for to = 1. You may use the partial fraction decomposition 1 + 52-58 +6 2 S-3 but you need to show all the steps needed to arrive to the expression 1 52-58 +6 in order to receive credit. f(t)=L-'{F(s) Table of Laplace...
Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer...
Use appropriate algebra and Theorem 7.2.1 to find the given
inverse Laplace transform. (Write your answer as a function of
t.)
ℒ−1 1/(s^2 + s − 56)
Some Inverse Transforms (a) 1 = L-1 (b) " = L-1 1 n = 1, 2, 3, ... (c) eat = L-1 L-1 (d) sin kt = L-1 k 92 + k? (e) cos kt = L- 52 + k ****] ) S (f) sinh kt = ! k 92 – k (g)...
Page 4 IV. (10) Use the Laplace transform to solve the IVP y" - 2y +...
Page 4 IV. (10) Use the Laplace transform to solve the IVP y" - 2y + y = f(t), y(0) = 1, y(0) = 1, where t<5 f(t) = t-5, t5 You may use the partial fraction decomposition 7(x2–2x+1) (6-1) + + - , but you need to show all the steps needed to arrive to the expression -16-28+1) in order to receive credit. f(t)=L-'{F(s) Table of Laplace Transforms F(s)=L{()} f(t)= L-'{F(s) F(s)=L{f(t)} 1. 2. et s-a 3. r", n=1,2,3,......
use Theorem 7.2 to find L{f(t)} (i have pictured the table of 7.2) ** just solve...
use
Theorem 7.2 to find L{f(t)} (i have pictured the table of 7.2)
** just solve #26 & #30 please!! NOT 28**
thank you!!
26. f(t) = (2t - 1) 28. f(t) = t - e-9 + 5 30. f(t) = (e' - e-)2 THEOREM 7.2 Transforms of Some Basic Functions (a) L{1} = 1 (b) L{t"} = 1 n = 1, 2, 3,... (C) L{e} = 1 (e) L{cos kt} = 2 * 2 (() {{sinh k} = 1...
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms...
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms of the given functions. (s > 0) 1 (s > 0) S- 1. Kt) = 12 2. f = 23t+1 Use transforms from the Table (op right) to find the Laplace transforms of the given functions. t" ( n20) (s > 0) r(a + 1) 1a (a > -1) (s > 0) 5+1 3. f(t) = VE +8t 4. f(t) = sin(2tcos(2t) Use the...
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0)...
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0) 5+1 T(a + 1) 1a (a > -1) (s > 0) $4+1 (s > 0) S-a 1. Let f(t) be a function on [0,-). Find the Laplace transform using the definition of the following functions: a. X(t) = 7t2 b. flt) 13t+18 2. Use the table to thexight to find the Laplace transform of the following function. a. f(t)=t-4e2t b. f(t) = (5 +t)2...
5) Using the table, find the Laplace inverse of S-3 F(s) = s2 - 2s +...
5) Using the table, find the Laplace inverse of S-3 F(s) = s2 - 2s + 4 Do not use line (16) in the table. Elementary Laplace Transforms Y(s) = LF0) = {e=f(e)dt 0 f(t) = ('{F(s)) F(s) = {f} f(t) = ('{F(s)} F(s) = {f} 1. 1 12. uct) -CS S> 0 S> 0 2. 1 S-a -F(s) 13. ue(t)f(t-c) S> a 3. th, nez* n! 14. ectf(t) F(s-c) S>0 s+ 14. t", p>-1 r(p+1) 15. f(ct) S> 0...
Differential equations 7.2 Inverse transforms and transforms of
derivatives
Use Laplace Transforms to solve the initial value problem y" + 4y = 25xe", y(0)=-2, and y'(0)=1. 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 +...
Differential equations 7.2 Inverse transforms and transforms of
derivatives
Use Laplace Transforms to solve the initial value problem y" – 2y'+5y=-25x , y(0)=2, and y'(0)=3. 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...
III. When solving this problem show all the steps needed to transform the expressions into ones that can be (10) found in the table and indicate the entry of the table used in each step. a) Find the Laplace transform F(s) of the function (5+234 +5e-2) cos(6t) b) Find the inverse Laplace transform f(t) of the function F(s) = 2 s2 + 2s + 5 f(t)=L-'{F(s) Table of Laplace Transforms F(s)=L{()} f(t)= L-'{F(s) F(s)=L{f(t)} 1. 2. et s-a 3. r",...
Page 2 II. (7) Use the Laplace transform to solve the IVP y" - 5y' + 6y = 8(t-1), y(0) = 0,0) = 0, where the right hand side is the Dirac Delta Function (t - to) for to = 1. You may use the partial fraction decomposition 1 + 52-58 +6 2 S-3 but you need to show all the steps needed to arrive to the expression 1 52-58 +6 in order to receive credit. f(t)=L-'{F(s) Table of Laplace...
Use appropriate algebra and Theorem 7.2.1 to find the given
inverse Laplace transform. (Write your answer as a function of
t.)
ℒ−1 1/(s^2 + s − 56)
Some Inverse Transforms (a) 1 = L-1 (b) " = L-1 1 n = 1, 2, 3, ... (c) eat = L-1 L-1 (d) sin kt = L-1 k 92 + k? (e) cos kt = L- 52 + k ****] ) S (f) sinh kt = ! k 92 – k (g)...
Page 4 IV. (10) Use the Laplace transform to solve the IVP y" - 2y + y = f(t), y(0) = 1, y(0) = 1, where t<5 f(t) = t-5, t5 You may use the partial fraction decomposition 7(x2–2x+1) (6-1) + + - , but you need to show all the steps needed to arrive to the expression -16-28+1) in order to receive credit. f(t)=L-'{F(s) Table of Laplace Transforms F(s)=L{()} f(t)= L-'{F(s) F(s)=L{f(t)} 1. 2. et s-a 3. r", n=1,2,3,......
use
Theorem 7.2 to find L{f(t)} (i have pictured the table of 7.2)
** just solve #26 & #30 please!! NOT 28**
thank you!!
26. f(t) = (2t - 1) 28. f(t) = t - e-9 + 5 30. f(t) = (e' - e-)2 THEOREM 7.2 Transforms of Some Basic Functions (a) L{1} = 1 (b) L{t"} = 1 n = 1, 2, 3,... (C) L{e} = 1 (e) L{cos kt} = 2 * 2 (() {{sinh k} = 1...
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms of the given functions. (s > 0) 1 (s > 0) S- 1. Kt) = 12 2. f = 23t+1 Use transforms from the Table (op right) to find the Laplace transforms of the given functions. t" ( n20) (s > 0) r(a + 1) 1a (a > -1) (s > 0) 5+1 3. f(t) = VE +8t 4. f(t) = sin(2tcos(2t) Use the...
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0) 5+1 T(a + 1) 1a (a > -1) (s > 0) $4+1 (s > 0) S-a 1. Let f(t) be a function on [0,-). Find the Laplace transform using the definition of the following functions: a. X(t) = 7t2 b. flt) 13t+18 2. Use the table to thexight to find the Laplace transform of the following function. a. f(t)=t-4e2t b. f(t) = (5 +t)2...
5) Using the table, find the Laplace inverse of S-3 F(s) = s2 - 2s + 4 Do not use line (16) in the table. Elementary Laplace Transforms Y(s) = LF0) = {e=f(e)dt 0 f(t) = ('{F(s)) F(s) = {f} f(t) = ('{F(s)} F(s) = {f} 1. 1 12. uct) -CS S> 0 S> 0 2. 1 S-a -F(s) 13. ue(t)f(t-c) S> a 3. th, nez* n! 14. ectf(t) F(s-c) S>0 s+ 14. t", p>-1 r(p+1) 15. f(ct) S> 0...
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