Skip to main content

Math Advanced Math ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

The value of y 1 ′ = 5 y 1 + y 2 , y 2 ′ = y 1 + 5 y 2 with initial condition y 1 ( 0 ) = 1 , y 2 ( 0 ) = − 3 . The solution of differential equation is y 1 = 2 e 4 t − e 6 t _ and y 2 = 29 e 6 t − 32 e 4 t _ . Formula used: Crammer rule: The solution of the equation a x + b y = e , c x + d y = f is x = | e b f d | | a b c d | , y = | a e c f | | a b c d | . Calculation: Taking the Laplace transform of the given differential equation y 1 ′ = 5 y 1 + y 2 . L [ y 1 ′ ] = L [ 5 y 1 + y 2 ] s L ( y 1 ) − y 1 ( 0 ) = 5 L ( y 1 ) + L ( y 2 ) ( s − 5 ) L ( y 1 ) − 1 = L ( y 2 ) ( s − 5 ) L ( y 1 ) − L ( y 2 ) = 1 Similarly, taking the Laplace transform of the given differential equation y 2 ′ = y 1 + 5 y 2 . L [ y 2 ′ ] = L [ y 1 + 5 y 2 ] s L ( y 2 ) − y 2 ( 0 ) = L ( y 1 ) + 5 L ( y 2 ) ( s − 5 ) L ( y 2 ) − L ( y 1 ) = y 2 ( 0 ) ( s − 5 ) L ( y 2 ) − L ( y 1 ) = − 3 By the use of Crammer rule, the value of L ( y 1 ) is calculated as: L ( y 1 ) = | 1 − 1 − 3 s − 5 | | s − 5 − 1 − 1 s − 5 | = ( s − 5 ) − 3 ( s − 5 ) 2 − 1 = ( s − 8 ) ( s − 5 ) 2 − 1 On the further simplification, the following is used. L ( y 1 ) = ( s − 8 ) ( ( s − 5 ) − 1 ) ( ( s − 5 ) + 1 ) = ( s − 8 ) ( s − 6 ) ( s − 4 ) = A ( s − 6 ) + B ( s − 4 ) The value of A calculated as: A = lim s → 6 [ ( s − 6 ) ( s − 8 ) ( s − 6 ) ( s − 4 ) ] = lim s → 6 [ ( s − 8 ) ( s − 4 ) ] = ( 6 − 8 ) ( 6 − 4 ) = − 1 The value of B calculated as: B = lim s → 4 [ ( s − 4 ) ( s − 8 ) ( s − 6 ) ( s − 4 ) ] = lim s → 4 [ ( s − 8 ) ( s − 6 ) ] = ( 4 − 8 ) ( 4 − 6 ) = 2 Substitute, the value of A and B in the equation ( s − 8 ) ( s − 6 ) ( s − 4 ) = A ( s − 6 ) + B ( s − 4 ) . ( s − 8 ) ( s − 6 ) ( s − 4 ) = − 1 ( s − 6 ) + 2 ( s − 4 ) = 2 ( s − 4 ) − 1 ( s − 6 ) Now the value of y 1 is calculated as: y 1 = L − 1 [ 2 ( s − 4 ) − 1 ( s − 6 ) ] = 2 e 4 t − e 6 t Substitute y 1 = 2 e 4 t − e 6 t in the equation y 1 ′ = 5 y 1 + y 2 . ( 2 e 4 t − e 6 t ) ′ = 5 ( 2 e 4 t − e 6 t ) + y 2 y 2 = 8 e 4 t − e 6 t − 40 e 4 t + 30 e 6 t y 2 = 29 e 6 t − 32 e 4 t Therefore, the solution of differential equation is y 1 = 2 e 4 t − e 6 t _ and y 2 = 29 e 6 t − 32 e 4 t _ .

The value of y 1 ′ = 5 y 1 + y 2 , y 2 ′ = y 1 + 5 y 2 with initial condition y 1 ( 0 ) = 1 , y 2 ( 0 ) = − 3 . The solution of differential equation is y 1 = 2 e 4 t − e 6 t _ and y 2 = 29 e 6 t − 32 e 4 t _ . Formula used: Crammer rule: The solution of the equation a x + b y = e , c x + d y = f is x = | e b f d | | a b c d | , y = | a e c f | | a b c d | . Calculation: Taking the Laplace transform of the given differential equation y 1 ′ = 5 y 1 + y 2 . L [ y 1 ′ ] = L [ 5 y 1 + y 2 ] s L ( y 1 ) − y 1 ( 0 ) = 5 L ( y 1 ) + L ( y 2 ) ( s − 5 ) L ( y 1 ) − 1 = L ( y 2 ) ( s − 5 ) L ( y 1 ) − L ( y 2 ) = 1 Similarly, taking the Laplace transform of the given differential equation y 2 ′ = y 1 + 5 y 2 . L [ y 2 ′ ] = L [ y 1 + 5 y 2 ] s L ( y 2 ) − y 2 ( 0 ) = L ( y 1 ) + 5 L ( y 2 ) ( s − 5 ) L ( y 2 ) − L ( y 1 ) = y 2 ( 0 ) ( s − 5 ) L ( y 2 ) − L ( y 1 ) = − 3 By the use of Crammer rule, the value of L ( y 1 ) is calculated as: L ( y 1 ) = | 1 − 1 − 3 s − 5 | | s − 5 − 1 − 1 s − 5 | = ( s − 5 ) − 3 ( s − 5 ) 2 − 1 = ( s − 8 ) ( s − 5 ) 2 − 1 On the further simplification, the following is used. L ( y 1 ) = ( s − 8 ) ( ( s − 5 ) − 1 ) ( ( s − 5 ) + 1 ) = ( s − 8 ) ( s − 6 ) ( s − 4 ) = A ( s − 6 ) + B ( s − 4 ) The value of A calculated as: A = lim s → 6 [ ( s − 6 ) ( s − 8 ) ( s − 6 ) ( s − 4 ) ] = lim s → 6 [ ( s − 8 ) ( s − 4 ) ] = ( 6 − 8 ) ( 6 − 4 ) = − 1 The value of B calculated as: B = lim s → 4 [ ( s − 4 ) ( s − 8 ) ( s − 6 ) ( s − 4 ) ] = lim s → 4 [ ( s − 8 ) ( s − 6 ) ] = ( 4 − 8 ) ( 4 − 6 ) = 2 Substitute, the value of A and B in the equation ( s − 8 ) ( s − 6 ) ( s − 4 ) = A ( s − 6 ) + B ( s − 4 ) . ( s − 8 ) ( s − 6 ) ( s − 4 ) = − 1 ( s − 6 ) + 2 ( s − 4 ) = 2 ( s − 4 ) − 1 ( s − 6 ) Now the value of y 1 is calculated as: y 1 = L − 1 [ 2 ( s − 4 ) − 1 ( s − 6 ) ] = 2 e 4 t − e 6 t Substitute y 1 = 2 e 4 t − e 6 t in the equation y 1 ′ = 5 y 1 + y 2 . ( 2 e 4 t − e 6 t ) ′ = 5 ( 2 e 4 t − e 6 t ) + y 2 y 2 = 8 e 4 t − e 6 t − 40 e 4 t + 30 e 6 t y 2 = 29 e 6 t − 32 e 4 t Therefore, the solution of differential equation is y 1 = 2 e 4 t − e 6 t _ and y 2 = 29 e 6 t − 32 e 4 t _ .

ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

10th Edition

ISBN: 9781119809210

Author: Kreyszig

Publisher: WILEY

See similar textbooks

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

Blurred answer

Chapter 6.7, Problem 5P

Chapter 6.7, Problem 7P

Students have asked these similar questions

Q/ By using polar Coordinates show that the system below has a limit cycle and show the stability of + his limit cycle: X² = x + x(x² + y² -1) y* = −x + y (x² + y²-1) -x

xy Q/Given H (X,Y) = ex-XX+1 be a first integral find the corresponding system and study the Stability of of critical point of this system.

Q/ show that H (X,Y) = x²-4x-x² is 2 first integral of the system Y° = y 0 y° = 2x + x 3 then study the stability of critical point and draw phase portrait.

Chapter 6 Solutions

ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE

Ch. 6.1 - Prob. 1P Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....

Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Find the transform. Show the details of your work....Ch. 6.1 - Table 6.1. Convert this table to a table for...Ch. 6.1 - Using in Prob. 10, find , where f1(t) = 0 if t ≦...Ch. 6.1 - Table 6.1. Derive formula 6 from formulas 9 and...Ch. 6.1 - Nonexistence. Show that does not satisfy a...Ch. 6.1 - Nonexistence. Give simple examples of functions...Ch. 6.1 - Existence. Show that . [Use (30) in App. 3.1.]...Ch. 6.1 - Change of scale. If and c is any positive...Ch. 6.1 - Inverse transform. Prove that is linear. Hint:...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - Given F(s) = ℒ(f), find f(t). a, b, L, n are...Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.1 - In Probs. 33–36 find the transform. In Probs....Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the IVPs by the Laplace transform. If...Ch. 6.2 - Solve the shifted data IVPs by the Laplace...Ch. 6.2 - Solve the shifted data IVPs by the Laplace...Ch. 6.2 - Solve the shifted data IVPs by the Laplace...Ch. 6.2 - Solve the shifted data IVPs by the Laplace...Ch. 6.2 - Using (1) or (2), find if f(t) equals: t cos 4t Ch. 6.2 - Using (1) or (2), find if f(t) equals: te−at Ch. 6.2 - Using (1) or (2), find if f(t) equals: cos2 2t Ch. 6.2 - Using (1) or (2), find if f(t) equals: sin2 ωt Ch. 6.2 - Using (1) or (2), find if f(t) equals: sin4 t....Ch. 6.2 - Using (1) or (2), find if f(t) equals: cosh2 t Ch. 6.2 - INVERSE TRANSFORMS BY INTEGRATION Using Theorem 3,...Ch. 6.2 - INVERSE TRANSFORMS BY INTEGRATION Using Theorem 3,...Ch. 6.2 - INVERSE TRANSFORMS BY INTEGRATION Using Theorem 3,...Ch. 6.2 - INVERSE TRANSFORMS BY INTEGRATION Using Theorem 3,...Ch. 6.2 - INVERSE TRANSFORMS BY INTEGRATION Using Theorem 3,...Ch. 6.2 - INVERSE TRANSFORMS BY INTEGRATION Using Theorem 3,...Ch. 6.2 - INVERSE TRANSFORMS BY INTEGRATION Using Theorem 3,...Ch. 6.3 - Report on Shifting Theorems. Explain and compare...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Sketch or graph the given function, which is...Ch. 6.3 - Find and sketch or graph f(t) if equals e−3s/(s −...Ch. 6.3 - Prob. 13P Ch. 6.3 - Prob. 14P Ch. 6.3 - Find and sketch or graph f(t) if equals e−3s/s4 Ch. 6.3 - Prob. 16P Ch. 6.3 - Prob. 17P Ch. 6.3 - Using the Laplace transform and showing the...Ch. 6.3 - Using the Laplace transform and showing the...Ch. 6.3 - Prob. 20P Ch. 6.3 - Using the Laplace transform and showing the...Ch. 6.3 - Using the Laplace transform and showing the...Ch. 6.3 - Prob. 23P Ch. 6.3 - Using the Laplace transform and showing the...Ch. 6.3 - Prob. 25P Ch. 6.3 - Prob. 26P Ch. 6.3 - Prob. 27P Ch. 6.3 - Prob. 28P Ch. 6.3 - Prob. 29P Ch. 6.3 - Prob. 30P Ch. 6.3 - Prob. 31P Ch. 6.3 - Prob. 32P Ch. 6.3 - Prob. 33P Ch. 6.3 - Prob. 34P Ch. 6.3 - Prob. 35P Ch. 6.3 - Prob. 36P Ch. 6.3 - Prob. 37P Ch. 6.3 - Prob. 38P Ch. 6.3 - Prob. 39P Ch. 6.3 - Prob. 40P Ch. 6.4 - Prob. 3P Ch. 6.4 - Prob. 4P Ch. 6.4 - Prob. 5P Ch. 6.4 - Prob. 6P Ch. 6.4 - Prob. 7P Ch. 6.4 - Prob. 8P Ch. 6.4 - Prob. 9P Ch. 6.4 - Prob. 11P Ch. 6.4 - Prob. 15P Ch. 6.5 - CONVOLUTIONS BY INTEGRATION Find: Ch. 6.5 - CONVOLUTIONS BY INTEGRATION Find: 2. Ch. 6.5 - CONVOLUTIONS BY INTEGRATION Find: 3. Ch. 6.5 - CONVOLUTIONS BY INTEGRATION Find: 4. Ch. 6.5 - Prob. 5P Ch. 6.5 - Prob. 6P Ch. 6.5 - Prob. 7P Ch. 6.5 - Prob. 8P Ch. 6.5 - Prob. 9P Ch. 6.5 - Prob. 10P Ch. 6.5 - Prob. 11P Ch. 6.5 - Prob. 12P Ch. 6.5 - Prob. 13P Ch. 6.5 - Prob. 14P Ch. 6.5 - CAS EXPERIMENT. Variation of a Parameter. (a)...Ch. 6.5 - Prob. 17P Ch. 6.5 - Prob. 18P Ch. 6.5 - Prob. 19P Ch. 6.5 - Prob. 20P Ch. 6.5 - Prob. 21P Ch. 6.5 - Prob. 22P Ch. 6.5 - Prob. 23P Ch. 6.5 - Prob. 24P Ch. 6.5 - Prob. 25P Ch. 6.5 - Prob. 26P Ch. 6.6 - Prob. 2P Ch. 6.6 - Prob. 3P Ch. 6.6 - Prob. 4P Ch. 6.6 - Prob. 5P Ch. 6.6 - Prob. 6P Ch. 6.6 - Prob. 7P Ch. 6.6 - Prob. 8P Ch. 6.6 - Prob. 9P Ch. 6.6 - Prob. 10P Ch. 6.6 - Prob. 11P Ch. 6.6 - Prob. 14P Ch. 6.6 - Prob. 15P Ch. 6.6 - Prob. 16P Ch. 6.6 - Prob. 17P Ch. 6.6 - Prob. 18P Ch. 6.6 - Prob. 19P Ch. 6.6 - Prob. 20P Ch. 6.7 - Prob. 2P Ch. 6.7 - Prob. 3P Ch. 6.7 - Prob. 4P Ch. 6.7 - Prob. 5P Ch. 6.7 - Prob. 6P Ch. 6.7 - Prob. 7P Ch. 6.7 - Prob. 8P Ch. 6.7 - Prob. 9P Ch. 6.7 - Prob. 10P Ch. 6.7 - Prob. 11P Ch. 6.7 - Prob. 12P Ch. 6.7 - Prob. 13P Ch. 6.7 - Prob. 14P Ch. 6.7 - Prob. 15P Ch. 6.7 - Prob. 16P Ch. 6.7 - Prob. 19P Ch. 6.7 - Prob. 20P Ch. 6 - Prob. 1RQ Ch. 6 - Prob. 2RQ Ch. 6 - Prob. 3RQ Ch. 6 - Prob. 4RQ Ch. 6 - Prob. 5RQ Ch. 6 - When and how do you use the unit step function and...Ch. 6 - If you know f(t) = ℒ−1{F(s)}, how would you find...Ch. 6 - Explain the use of the two shifting theorems from...Ch. 6 - Prob. 9RQ Ch. 6 - Prob. 10RQ Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the transform, indicating the method used and...Ch. 6 - Find the inverse transform, indicating the method...Ch. 6 - Prob. 21RQ Ch. 6 - Prob. 22RQ Ch. 6 - Prob. 23RQ Ch. 6 - Prob. 24RQ Ch. 6 - Prob. 25RQ Ch. 6 - Prob. 26RQ Ch. 6 - Prob. 27RQ Ch. 6 - Prob. 28RQ Ch. 6 - Prob. 29RQ Ch. 6 - Prob. 30RQ Ch. 6 - Prob. 31RQ Ch. 6 - Prob. 32RQ Ch. 6 - Prob. 33RQ Ch. 6 - Prob. 34RQ Ch. 6 - Prob. 35RQ Ch. 6 - Prob. 36RQ Ch. 6 - Prob. 37RQ Ch. 6 - Prob. 38RQ Ch. 6 - Prob. 39RQ Ch. 6 - Prob. 40RQ Ch. 6 - Prob. 41RQ Ch. 6 - Prob. 42RQ Ch. 6 - Prob. 43RQ Ch. 6 - Prob. 44RQ Ch. 6 - Prob. 45RQ

Knowledge Booster

Background pattern image

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Basic Technical Mathematics
Advanced Math
ISBN:9780134437705
Author:Washington
Publisher:PEARSON
Topology
Advanced Math
ISBN:9780134689517
Author:Munkres, James R.
Publisher:Pearson,

Text book image

Advanced Engineering Mathematics

Advanced Math

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Wiley, John & Sons, Incorporated

Text book image

Numerical Methods for Engineers

Advanced Math

ISBN:9780073397924

Author:Steven C. Chapra Dr., Raymond P. Canale

Publisher:McGraw-Hill Education

Text book image

Introductory Mathematics for Engineering Applicat...

Advanced Math

ISBN:9781118141809

Author:Nathan Klingbeil

Publisher:WILEY

Text book image

Mathematics For Machine Technology

Advanced Math

ISBN:9781337798310

Author:Peterson, John.

Publisher:Cengage Learning,

Text book image

Basic Technical Mathematics

Advanced Math

ISBN:9780134437705

Author:Washington

Publisher:PEARSON

Text book image

Advanced Math

ISBN:9780134689517

Author:Munkres, James R.

Publisher:Pearson,

SEE MORE TEXTBOOKS