Solve the Initial Value Problem $$( x + 3 ) \frac { d y } { d x } - 2 \left( x ^ { 2 } + 3 x \right) y = \frac { e ^ { x ^ { 2 } } } { x + 3 } ; x > - 3 , y ( 0 ) = 0$$

question 85

Multiple Choice

Solve the initial value problem.
- $$( x + 3 ) \frac { d y } { d x } - 2 \left( x ^ { 2 } + 3 x \right) y = \frac { e ^ { x ^ { 2 } } } { x + 3 } ; x > - 3 , y ( 0 ) = 0$$

• A) \(y = - e ^ {- x ^ { 2 } } \left( \frac { x } { 3 x + 9 } \right) , x > - 3\)
• B) \(y = e ^ { x ^ { 2 } } \left( \frac { x } { 3 x + 9 } \right) , x > - 3\)
• C) \(y = - e ^ { x 2 } \left( \frac { x } { 3 x + 9 } \right) , x > - 3\)
• D) \(y = e ^ { - x ^ { 2 } } \left( \frac { x } { 3 x + 9 } \right) , x > - 3\)

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Definitions:

Generality

The extent to which findings, principles, or theories are applicable across a wide range of situations, conditions, or groups.

Ethicality

The degree to which an action or decision is morally acceptable, following established ethical standards.

Cost

The required expenditure or investment of resources, such as time, money, or effort, in order to obtain a product or achieve an objective.

Strong Manipulation

An experimental approach that involves significant alterations to the independent variable to observe a clear effect on the dependent variable.