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Page 2 II. (7) Use the Laplace transform to solve the IVP y" - 5y' +...
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,......
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 3 Name (please print) III (10) When solving this problem show all the steps needed...
Page 3 Name (please print) III (10) When solving this problem show all the steps needed to transform the expressions into ones that can be 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 (3-24 + 5e") sin(Tt) b) Find the inverse Laplace transform f(t) of the function F(s) = 9 32 +8-20 S()--'{F(s) 1. i Table of Laplace Transforms F(x) = {/0) (1)-2-(F) F(s)-...
Solve the given initial value problem using the method of Laplace transforms. y'' + 3y' +2y...
Solve the given initial value problem using the method of Laplace transforms. y'' + 3y' +2y = tu(t-3); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem. y(t) = | Properties of Laplace Transforms L{f+g} = £{f} + L{g} L{cf} = CL{f} for any constant £{e atf(t)} (s) = L{f}(s-a) L{f'}(s) = sL{f}(s) – f(0) L{f''}(s) =...
Elementary Laplace Transtorms Y(S) = {f} -L e-stf(t)dt fc = C-'{F(s)} F(s) = {f} f(t) =-'{F(s))...
Elementary Laplace Transtorms Y(S) = {f} -L e-stf(t)dt fc = C-'{F(s)} F(s) = {f} f(t) =-'{F(s)) F(s) = {f} -CS 1. 1 1 12. uct) le S> 0 S> 0 . s S 2. eat 1 13. ucOf(t-c) e-csF(s) S> a S-a n! 3. t",n e Z 14. ectf(t) F( sc) S> 0 sh+1 4. tP, p>-1 (p+1) S> 0 SP+1 15. f(ct) F). c>0 16. SFt - 1)g(t)dt F(s)G(*) 5. sin at S> 0 16. cos at 17. 8(t...
Detailed answer using the Laplace Transforms method Solve the IVP using the method of Laplace transforms...
Detailed answer using the Laplace Transforms method
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
Elementary Laplace Transtorms Y(S) = {f} -L e-stf(t)dt fc = C-'{F(s)} F(s) = {f} f(t) =-'{F(s))...
Elementary Laplace Transtorms Y(S) = {f} -L e-stf(t)dt fc = C-'{F(s)} F(s) = {f} f(t) =-'{F(s)) F(s) = {f} -CS 1. 1 1 12. uct) le S> 0 S> 0 . s S 2. eat 1 13. ucOf(t-c) e-csF(s) S> a S-a n! 3. t",n e Z 14. ectf(t) F( sc) S> 0 sh+1 4. tP, p>-1 (p+1) S> 0 SP+1 15. f(ct) F). c>0 16. SFt - 1)g(t)dt F(s)G(*) 5. sin at S> 0 16. cos at 17. 8(t...
Detailed answer with another method then the Laplace transforms Solve the IVP using the method of...
Detailed answer with another method then the Laplace
transforms
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0...
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...
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,......
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 3 Name (please print) III (10) When solving this problem show all the steps needed to transform the expressions into ones that can be 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 (3-24 + 5e") sin(Tt) b) Find the inverse Laplace transform f(t) of the function F(s) = 9 32 +8-20 S()--'{F(s) 1. i Table of Laplace Transforms F(x) = {/0) (1)-2-(F) F(s)-...
Solve the given initial value problem using the method of Laplace transforms. y'' + 3y' +2y = tu(t-3); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem. y(t) = | Properties of Laplace Transforms L{f+g} = £{f} + L{g} L{cf} = CL{f} for any constant £{e atf(t)} (s) = L{f}(s-a) L{f'}(s) = sL{f}(s) – f(0) L{f''}(s) =...
Elementary Laplace Transtorms Y(S) = {f} -L e-stf(t)dt fc = C-'{F(s)} F(s) = {f} f(t) =-'{F(s)) F(s) = {f} -CS 1. 1 1 12. uct) le S> 0 S> 0 . s S 2. eat 1 13. ucOf(t-c) e-csF(s) S> a S-a n! 3. t",n e Z 14. ectf(t) F( sc) S> 0 sh+1 4. tP, p>-1 (p+1) S> 0 SP+1 15. f(ct) F). c>0 16. SFt - 1)g(t)dt F(s)G(*) 5. sin at S> 0 16. cos at 17. 8(t...
Detailed answer using the Laplace Transforms method
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
Elementary Laplace Transtorms Y(S) = {f} -L e-stf(t)dt fc = C-'{F(s)} F(s) = {f} f(t) =-'{F(s)) F(s) = {f} -CS 1. 1 1 12. uct) le S> 0 S> 0 . s S 2. eat 1 13. ucOf(t-c) e-csF(s) S> a S-a n! 3. t",n e Z 14. ectf(t) F( sc) S> 0 sh+1 4. tP, p>-1 (p+1) S> 0 SP+1 15. f(ct) F). c>0 16. SFt - 1)g(t)dt F(s)G(*) 5. sin at S> 0 16. cos at 17. 8(t...
Detailed answer with another method then the Laplace
transforms
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt 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...
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