The Solution of the Eigenvalue Problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( 1 ) = 0$

question 27

Multiple Choice

The solution of the eigenvalue problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( 1 ) = 0$ is

• A) \(\lambda = n \pi , y = \cos ( n \pi x ) , n = 0,1,2 , \ldots\)
• B) \(\lambda = n \pi , y = \sin ( n \pi x ) , n = 1,2,3 , \ldots\)
• C) \(\lambda = n ^ { 2 } \pi ^ { 2 } , y = \cos ( n \pi x ) , n = 0,1,2 , \ldots\)
• D) \(\lambda = n ^ { 2 } \pi ^ { 2 } , y = \sin ( n \pi x ) , n = 1,2,3 , \ldots\)
• E) \(\lambda = n \pi , y = \cos ( n \pi x ) + \sin ( n \pi x ) , n = 1,2,3 , \ldots\)

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Definitions:

Ronald Reagan

The 40th President of the United States (1981-1989) known for his economic policies known as "Reaganomics," the end of the Cold War, and conservative political ideology.

Herbert Hoover

The 31st President of the United States (1929-1933), whose term was notably marked by the onset of the Great Depression.

Great Depression

A severe worldwide economic downturn that took place during the 1930s, characterized by high unemployment, deflation, and a significant fall in economic activity.

Economic Expansion

A phase of the business cycle where the economy grows and increases its output, leading to higher employment and income levels.