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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