Use Power Series to Solve the Differential Equation $$y ^ { \prime \prime } + x ^ { 2 } y = 0 , y ( 0 ) = 6 , y ^ { t } ( 0 ) = 0$$

question 158

Multiple Choice

Use power series to solve the differential equation.
$$y ^ { \prime \prime } + x ^ { 2 } y = 0 , y ( 0 ) = 6 , y ^ { t } ( 0 ) = 0$$

• A)
• \[y ( x ) = 6 - \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\]
• B)
• \[y ( x ) = \sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { 6 x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\]
• C)
• \[y ( x ) = 6 + \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { 6 x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\]
• D)
• \[y ( x ) = - 6 + \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\]
• E)
• \[y ( x ) = \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\]

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Id

In psychoanalytic theory, the part of the personality that is the source of instinctual impulses and demands for immediate satisfaction of primitive needs.

Psychosexual Stages

A theory by Sigmund Freud that describes the development of human personality and behavior in terms of a series of stages during childhood, each characterized by a specific erogenous zone and conflict.

Oral

The first stage of Freud's psychosexual development, where pleasure centers on activities involving the mouth.

Phallic

Relating to or resembling a phallus, often used in the context of Freudian psychoanalysis to describe the stage of child development focused on the genitals.