Solve the Initial Value Problem for X as a Function $$\left( t ^ { 2 } + 2 t \right) \frac { d x } { d t } = 2 x + 8 , x ( 1 ) = 1$$

question 413

Multiple Choice

Solve the initial value problem for x as a function of t.
- $$\left( t ^ { 2 } + 2 t \right) \frac { d x } { d t } = 2 x + 8 , x ( 1 ) = 1$$

• A) \(x = 15 \ln \left| \frac { t } { t + 2 } \right| - 4\)
• B) \(x = \frac { 14 t } { t + 2 } - 4\)
• C) \(x = \frac { 15 t } { t + 2 } - 4\)
• D) \(x = 15 t + \ln | t + 2 | - 4\)

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Definitions:

Perfectly Elastic

Describes a market condition where demand or supply responds instantaneously to changes in price with an infinite change in quantity demanded or supplied, depicted as a horizontal line in graphical analysis.

Elasticity of Demand

A measure of how much the quantity demanded of a good responds to a change in the price of that good, reflecting consumer sensitivity to price changes.

Horizontal Line

A straight line that has a constant y-value in the plane Cartesian coordinate system, indicating no change in the vertical direction.

Inferior Goods

For inferior goods, demand decreases as income increases.