Solve the Initial Value Problem $$( x + 4 ) \frac { d y } { d x } - 2 \left( x ^ { 2 } + 4 x \right) y = \frac { e ^ { x ^ { 2 } } } { x + 4 } ; x > - 4 , y ( 0 ) = 0$$

question 48

Multiple Choice

Solve the initial value problem.
- $$( x + 4 ) \frac { d y } { d x } - 2 \left( x ^ { 2 } + 4 x \right) y = \frac { e ^ { x ^ { 2 } } } { x + 4 } ; x > - 4 , y ( 0 ) = 0$$

• A) \(y = e ^ { x ^ { 2 } } \left( \frac { x } { 4 x + 16 } \right) , x > - 4\)
• B) \(y = - e ^ { x ^ { 2 } } \left( \frac { x } { 4 x + 16 } \right) , x > - 4\)
• C) \(y = e ^ { - x ^ { 2 } } \left( \frac { x } { 4 x + 16 } \right) , x > - 4\)
• D) \(y = - e ^ { - x ^ { 2 } } \left( \frac { x } { 4 x + 16 } \right) , x > - 4\)

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Definitions:

Voluntary Behaviors

Actions that are performed consciously and willingly by individuals.

Reinforcers

Stimuli or events that increase the likelihood of the behavior that they follow, used in operant conditioning.

Law Of Effect

Thorndike’s principle that behaviors followed by favorable consequences become more likely, and that behaviors followed by unfavorable consequences become less likely.

Shaping

A behavioral psychology technique of progressively reinforcing behaviors that approximate or lead towards a desired goal behavior.