Find the Solution of the Initial-Value Problem $\frac { d y } { d t } = \frac { y + t ^ { 2 } y } { t ^ { 2 } }$

question 99

Multiple Choice

Find the solution of the initial-value problem $\frac { d y } { d t } = \frac { y + t ^ { 2 } y } { t ^ { 2 } }$ , $y ( 1 ) = 2$ .

• A) \(y = 2 e ^ { t + ( 1 / t ) }\)
• B) \(y = 3 e ^ { t - ( 1 / t ) }\)
• C) \(y = 2 e ^ { t }\)
• D) \(y = 2 e ^ { 1 + \left( 1 / t ^ { 2 } \right) }\)
• E) \(y = 2 e ^ { 1 / t }\)
• F) \(y = c e ^ { t - ( 1 / t ) }\)
• G) \(y = c e ^ { t + ( 1 / t ) }\)
• H) \(y = 2 e ^ { t - ( 1 / t ) }\)

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Definitions:

Markup

The amount added to the cost of a product to determine the selling price, typically expressed as a percentage of the cost.

Machine-Hours

An indicator of manufacturing productivity that calculates the total hours machinery is active in the production cycle.

Manufacturing Overhead

Refers to all the costs associated with the manufacturing process except for direct materials and direct labor.

Variable Manufacturing Overhead

Variable manufacturing overhead includes expenses that fluctuate with production levels, such as materials and utility costs directly associated with manufacturing.