The linear differential equation y ″ + λ y = 0 subjected to y ( 0 ) = 0 and y ( 1 ) + y ′ ( 1 ) = 0 satisfies ‖ sin α n x ‖ 2 = 1 2 [ 1 + cos 2 α n ] .

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Answer 1

Question

Chapter 12.5, Problem 6E

To determine

To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

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Answer 2

Question

Chapter 12.5, Problem 6E

To determine

To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

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Answer 3

Question

Chapter 12.5, Problem 6E

To determine

To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

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Answer 4

Question

Chapter 12.5, Problem 6E

To determine

To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

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Answer 5

Chapter 12.5, Problem 6E

To determine

To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

Answer 6

Chapter 12.5, Problem 6E

To determine

To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

Answer 7

Chapter 12.5, Problem 6E

To determine

To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E

The linear differential equation y ″ + λ y = 0 subjected to y ( 0 ) = 0 and y ( 1 ) + y ′ ( 1 ) = 0 satisfies ‖ sin α n x ‖ 2 = 1 2 [ 1 + cos 2 α n ] .

Solution Summary: The author explains that the linear differential equation y′′+lambda y=0 satisfies the Eigen function of the above equation obtained from example 2.

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To show: The linear differential equation y″+λy=0 subjected to y(0)=0 and y(1)+y′(1)=0 satisfies ‖sinαnx‖2=12[1+cos2αn].

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Chapter 12 Solutions