Solve the Initial Value Problem for X as a Function $$\left( 2 t ^ { 3 } - 2 t ^ { 2 } + t - 1 \right) \frac { d x } { d t } = 3 , x ( 2 ) = 0$$

question 117

Multiple Choice

Solve the initial value problem for x as a function of t.
- $$\left( 2 t ^ { 3 } - 2 t ^ { 2 } + t - 1 \right) \frac { d x } { d t } = 3 , x ( 2 ) = 0$$

• A) \(x = \ln | t - 1 | - \frac { 1 } { 2 } \ln \left| t ^ { 2 } + \frac { 1 } { 2 } \right| + \frac { 1 } { 2 } \ln 4.5\)
• B) \(x = \ln | t - 1 | - \sqrt { 2 } \tan ^ { - 1 } \sqrt { 2 } t + \sqrt { 2 } \tan ^ { - 1 } 2 \sqrt { 2 }\)
• C) \(x = \ln | t - 1 | - \tan ^ { - 1 } \sqrt { 2 } t - \ln \left| t ^ { 2 } + \frac { 1 } { 2 } \right| + \tan ^ { - 1 } 2 \sqrt { 2 } + \ln 4.5\)
• D) \(x = \ln | t - 1 | - \sqrt { 2 } \tan ^ { - 1 } \sqrt { 2 } t - \frac { 1 } { 2 } \ln \left| t ^ { 2 } + \frac { 1 } { 2 } \right| + \sqrt { 2 } \tan ^ { - 1 } 2 \sqrt { 2 } + \frac { 1 } { 2 } \ln 4.5\)

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Definitions:

Income Distribution

Income Distribution refers to the way in which total income is shared among the members of a society.

Capital Flow

The movement of money for the purpose of investment, trade, or business production, either within a country (domestic capital flow) or across national borders (international capital flow).

Excess Profits

Profits that exceed the normal expected return on investment, often resulting from monopolistic or oligopolistic market structures.

General Equilibrium

A condition in an economy where supply and demand are balanced across all markets simultaneously.