Solve the Initial-Value Problem $$r ^ { t } + 2 t r = r , \quad r ( 0 ) = 6$$

question 42

Multiple Choice

Solve the initial-value problem.
$$r ^ { t } + 2 t r = r , \quad r ( 0 ) = 6$$

• A)
• \[r ( t ) = \frac { e ^ { t ^ { 2 } } } { 6 }\]
• B) \(r ( t ) = 6 e ^ { t - t ^ { 2 } }\)
• C) \(r ( t ) = e ^ { t - 6 t ^ { 2 } }\)
• D) \(r ( t ) = 6 e ^ { t - 2 t }\)
• E) \(r ( t ) = 6 e ^ { 2 t }\)

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Definitions:

Mouth

The location where a stream, river, or canyon ends, such as where a river enters the sea.

Cross-sectional Area

The area of an object or space as seen from a cut through the object, typically perpendicular to its longest dimension.

Volume

Volume is a measure of the amount of space that an object or substance occupies, commonly expressed in cubic units.

Maximum Sediment Grain Size

The largest diameter of individual grains in a sedimentary deposit, indicating the energy of the transporting medium.