The Initial Value Problem $x ^ { \prime \prime } - x ^ { \prime } + t x = 0 , x ( 0 ) = 1 , x ^ { \prime } ( 0 ) = 2$

question 29

Multiple Choice

The initial value problem $x ^ { \prime \prime } - x ^ { \prime } + t x = 0 , x ( 0 ) = 1 , x ^ { \prime } ( 0 ) = 2$ can be rewritten as the system

• A) \(x ^ { \prime } = x , u ^ { \prime } = u - t x , x ( 0 ) = 1 , u ( 0 ) = 2\)
• B) \(x ^ { \prime } = x , u ^ { \prime } = x - t u , x ( 0 ) = 1 , u ( 0 ) = 2\)
• C) \(x ^ { \prime } = u , u ^ { \prime } = u + t x , x ( 0 ) = 1 , u ( 0 ) = 2\)
• D) \(x ^ { \prime } = u , u ^ { \prime } = x + t u , x ( 0 ) = 1 , u ( 0 ) = 2\)
• E) \(x ^ { \prime } = u , u ^ { \prime } = u - t x , x ( 0 ) = 1 , u ( 0 ) = 2\)

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Definitions:

Elastic Demand

A situation where the quantity demanded of a good or service significantly changes in response to a change in its price, indicating a high price sensitivity.

Inelastic Demand

Refers to a situation where the demand for a product is relatively unresponsive to changes in price.

Inelastic Demand

A situation where the demand for a product does not significantly change with a change in price.

Good Substitutes

Products or services that can be used in place of each other, with consumers willing to switch from one to the other if the price or quality changes.