Find the Solution of the Initial-Value Problem $\frac { d y } { d t } = 3 y + 1$

Find the solution of the initial-value problem $\frac { d y } { d t } = 3 y + 1$ , $y ( 0 ) = 2$ .

A) $y = \frac { 1 } { 3 } \left( 7 e ^ { t } - 1 \right)$
B) $y = \left( 7 e ^ { t } - 5 \right)$
C) $y = \frac { 1 } { 3 } \left( e ^ { 3 t } - 1 \right)$
D) $y = \left( 3 e ^ { 3 t } - 1 \right)$
E) $y = \frac { 1 } { 3 } \left( 5 e ^ { 3 t } + 1 \right)$
F) $y = \left( 5 e ^ { 3 t } + 1 \right)$
G) $y = \frac { 1 } { 3 } \left( 7 e ^ { 3 t } - 1 \right)$
H) $y = \left( 7 e ^ { 3 t } - 1 \right)$

Correct Answer:

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