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

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) $y = 2 e ^ { t - ( 1 / t ) }$

Correct Answer:

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