Solve the Initial Value Problem $$\frac { d y } { d x } = \sin ( 4 x + \pi ) , y ( 0 ) = 2$$

question 2

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d x } = \sin ( 4 x + \pi ) , y ( 0 ) = 2$$

• A) \(y = - \cos ( 4 x + \pi ) + 1\)
• B) \(\mathrm { y } = - \frac { 1 } { 4 } \cos ( 4 \mathrm { x } + \pi ) + \frac { 7 } { 4 }\)
• C) \(y = 4 \cos ( 4 x + \pi ) + 2\)
• D) \(y = - \frac { 1 } { 4 } \cos ( 4 x + \pi ) + 2\)

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Definitions:

Domain

The set of all possible input values for which a function is defined.

Rational Function

A function represented by the quotient of two polynomials, where the denominator is not zero.

Rational Expression

A ratio of two polynomial expressions, with a non-zero denominator.

Simplify

To reduce an expression or equation to its simplest form by performing all possible operations and combining like terms.