Solve the Initial Value Problem for Y as a Function $$\left( x ^ { 2 } + 49 \right) \frac { d y } { d x } = 1 , y ( 7 ) = 0$$

question 337

Multiple Choice

Solve the initial value problem for y as a function of x.
- $$\left( x ^ { 2 } + 49 \right) \frac { d y } { d x } = 1 , y ( 7 ) = 0$$

• A) \(y = \frac { 1 } { 7 } \tan ^ { - 1 } \frac { x } { 7 } - \frac { \pi } { 28 }\)
• B) \(y = \frac { 1 } { 7 } \tan ^ { - 1 } \frac { x } { 7 }\)
• C) \(y = \frac { x } { 7 } - 1\)
• D) \(y = \frac { 1 } { 7 } \sin ^ { - 1 } \frac { x } { 7 } - \frac { \pi } { 14 }\)

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Definitions:

Developmental Changes

The transformation or evolution of physical, cognitive, psychological, and social capabilities and functioning over the course of a person's lifetime.

Sensorimotor Stage

A stage in Piaget's theory of cognitive development, occurring from birth to about 2 years of age, where infants learn about the world through their senses and motor actions.

Piaget's Stage

Refers to one of the developmental phases in Piaget's theory of cognitive development, highlighting key milestones in a child's learning and understanding.

Preoperational

The second stage in Piaget's theory of cognitive development, characterized by symbolic thought and egocentrism, typically occurring from ages 2 to 7.