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Math Advanced Math Custom Kreyszig: Advanced Engineering Mathematics

Whether the function cosh 2 x , sinh 2 x , e 2 x linearly independent or dependent on the half-axis. The function y 1 , y 2 and y 3 are linearly dependent _ . Formula used: The Wronskian W of n solutions y 1 , ⋅ ⋅ ⋅ , y n defined as the n th − order determinant is W ( y 1 , ⋅ ⋅ ⋅ , y n ) = | y 1 y 2 ⋅ ⋅ ⋅ y n y 1 ′ y 2 ′ ⋅ ⋅ ⋅ y 2 ′ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ y 1 ( n − 1 ) y 2 ( n − 1 ) ⋅ ⋅ ⋅ y n ( n − 1 ) | . Calculation: Suppose that the given function y 1 = cosh 2 x , y 2 = sinh 2 x and y 3 = e 2 x . Substitute, y 1 = cosh 2 x and y 2 = sinh 2 x in the expression y 1 + y 2 . y 1 + y 2 = cosh 2 x + sinh 2 x = e 2 x + e − 2 x 2 + e 2 x − e − 2 x 2 = 2 e 2 x 2 On the further simplification, the following is obtained. y 1 + y 2 = e 2 x = y 3 From the above calculation, it can be observed that e 2 x is the linear combination of other two functions. Therefore, the function y 1 , y 2 and y 3 are linearly dependent _ .

Whether the function cosh 2 x , sinh 2 x , e 2 x linearly independent or dependent on the half-axis. The function y 1 , y 2 and y 3 are linearly dependent _ . Formula used: The Wronskian W of n solutions y 1 , ⋅ ⋅ ⋅ , y n defined as the n th − order determinant is W ( y 1 , ⋅ ⋅ ⋅ , y n ) = | y 1 y 2 ⋅ ⋅ ⋅ y n y 1 ′ y 2 ′ ⋅ ⋅ ⋅ y 2 ′ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ y 1 ( n − 1 ) y 2 ( n − 1 ) ⋅ ⋅ ⋅ y n ( n − 1 ) | . Calculation: Suppose that the given function y 1 = cosh 2 x , y 2 = sinh 2 x and y 3 = e 2 x . Substitute, y 1 = cosh 2 x and y 2 = sinh 2 x in the expression y 1 + y 2 . y 1 + y 2 = cosh 2 x + sinh 2 x = e 2 x + e − 2 x 2 + e 2 x − e − 2 x 2 = 2 e 2 x 2 On the further simplification, the following is obtained. y 1 + y 2 = e 2 x = y 3 From the above calculation, it can be observed that e 2 x is the linear combination of other two functions. Therefore, the function y 1 , y 2 and y 3 are linearly dependent _ .

Custom Kreyszig: Advanced Engineering Mathematics

Custom Kreyszig: Advanced Engineering Mathematics

10th Edition

ISBN: 9781119166856

Author: Kreyszig

Publisher: JOHN WILEY+SONS INC.CUSTOM

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Custom Kreyszig: Advanced Engineering Mathematics

Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P Ch. 3.1 - Prob. 11P

Ch. 3.1 - Prob. 12P Ch. 3.1 - Prob. 13P Ch. 3.1 - Prob. 14P Ch. 3.1 - Prob. 15P Ch. 3.1 - Prob. 16P Ch. 3.2 - Prob. 1P Ch. 3.2 - Prob. 2P Ch. 3.2 - Solve the given ODE. Show the details of your...Ch. 3.2 - Solve the given ODE. Show the details of your...Ch. 3.2 - Solve the given ODE. Show the details of your...Ch. 3.2 - Solve the given ODE. Show the details of your...Ch. 3.2 - Solve the IVP by a CAS, giving a general solution...Ch. 3.2 - Prob. 8P Ch. 3.2 - Solve the IVP by a CAS, giving a general solution...Ch. 3.2 - Solve the IVP by a CAS, giving a general solution...Ch. 3.2 - Solve the IVP by a CAS, giving a general solution...Ch. 3.2 - CAS EXPERIMENT. Reduction of Order. Starting with...Ch. 3.3 - Solve the following ODEs, showing the details of...Ch. 3.3 - Solve the following ODEs, showing the details of...Ch. 3.3 - Solve the following ODEs, showing the details of...Ch. 3.3 - Solve the following ODEs, showing the details of...Ch. 3.3 - Prob. 5P Ch. 3.3 - Prob. 6P Ch. 3.3 - Solve the following ODEs, showing the details of...Ch. 3.3 - Solve the given IVP, showing the details of your...Ch. 3.3 - Solve the given IVP, showing the details of your...Ch. 3.3 - Prob. 10P Ch. 3.3 - Solve the given IVP, showing the details of your...Ch. 3.3 - Solve the given IVP, showing the details of your...Ch. 3.3 - Solve the given IVP, showing the details of your...Ch. 3 - Prob. 1RQ Ch. 3 - List some other basic theorems that extend from...Ch. 3 - If you know a general solution of a homogeneous...Ch. 3 - What form does an initial value problem for an...Ch. 3 - What is the Wronskian? What is it used for? Ch. 3 - Prob. 6RQ Ch. 3 - Solve the given ODE. Show the details of your...Ch. 3 - Solve the given ODE. Show the details of your...Ch. 3 - Prob. 9RQ Ch. 3 - Solve the given ODE. Show the details of your...Ch. 3 - Solve the given ODE. Show the details of your...Ch. 3 - Prob. 12RQ Ch. 3 - Solve the given ODE. Show the details of your...Ch. 3 - Prob. 14RQ Ch. 3 - Prob. 15RQ Ch. 3 - Solve the IVP. Show the details of your work. Ch. 3 - Solve the IVP. Show the details of your work. y‴ +...Ch. 3 - Solve the IVP. Show the details of your work. Ch. 3 - Solve the IVP. Show the details of your work. Ch. 3 - Solve the IVP. Show the details of your work.

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