Find the Particular Solution of the Given Differential Equation That $\frac { d y } { d x } = y ^ { 2 } \sqrt { 6 - x }$

question 17

Multiple Choice

Find the particular solution of the given differential equation that satisfies the indicated condition: $\frac { d y } { d x } = y ^ { 2 } \sqrt { 6 - x }$ ; y = 1 when x = 6.

• A) \(y = \frac { 2 ( 6 - x ) ^ { 3 / 2 } - 3 } { 3 }\)
• B) \(y = \frac { 3 } { 2 ( 6 + x ) ^ { 3 / 2 } - 3 }\)
• C) \(y = \frac { 3 } { 2 ( 6 - x ) ^ { 3 / 2 } - 3 }\)
• D) \(y = \frac { 3 } { 2 ( 6 - x ) ^ { 3 / 2 } + 3 }\)

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Definitions:

Conscious Awareness

The state of being cognitively awake and aware of one's internal and external environments.

Memories

The faculty by which the mind stores and remembers information; also refers to the mental record of past experiences.

Reality Principle

A concept in psychoanalytic theory representing the ability of the mind to assess the external world and act upon it accordingly, as opposed to the pleasure principle.

Ego

In psychoanalytic theory, the part of the personality that deals with the reality of the world and tries to meet the needs of the id in socially acceptable ways.