Solve the Initial Value Problem $$\frac { d y } { d x } = 12 ( 4 x - 5 ) ^ { - 6 } , \quad y ( 0 ) = 1$$

question 226

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d x } = 12 ( 4 x - 5 ) ^ { - 6 } , \quad y ( 0 ) = 1$$

• A) \(y = - \frac { 3 } { 5 } ( 4 x - 5 ) ^ { - 5 } + 1\)
• B) \(y = ( 4 x - 5 ) ^ { - 5 } - 5\)
• C) \(y = - \frac { 12 } { 5 } ( 4 x - 5 ) ^ { - 5 } + 1\)
• D) \(y = - \frac { 3 } { 7 } ( 4 x - 5 ) ^ { - 7 } + 1\)

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Definitions:

Schemes

In cognitive development, structured patterns of thought or behavior that individuals use to make sense of their experiences, often evolving with new information.

Cognition

The mental action or process of acquiring knowledge and understanding through thought, experience, and the senses, encompassing processes such as memory, judgment, and problem-solving.

Reflexes

Involuntary responses or actions that are automatic and occur without conscious thought in reaction to specific stimuli.

Conservation Skills

The cognitive ability to understand that quantity remains the same despite changes in shape or appearance, typically developing in early childhood.