Solve the Initial Value Problem Initial Condition $\mathbf { r } ( 0 ) = - 4 \mathbf { j }$

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = \left( \sec ^ { 2 } \mathrm { t } \right) \mathbf { i } + \left( 4 \mathrm { t } ^ { 3 } - 6 \right) \mathbf { j }$
Initial Condition: $\mathbf { r } ( 0 ) = - 4 \mathbf { j }$

A) $\mathbf { r } ( \mathrm { t } ) = ( - \tan \mathrm { t } ) \mathbf { i } + \left( 12 \mathrm { t } ^ { 2 } - 4 \right) \mathbf { j }$
B) $\mathbf { r } ( \mathrm { t } ) = ( \tan t ) \mathbf { i } + \left( \mathrm { t } ^ { 4 } \right) \mathbf { j }$
C) $\mathbf { r } ( \mathrm { t } ) = ( \tan \mathrm { t } ) \mathbf { i } + \left( \mathrm { t } ^ { 4 } - 4 \right) \mathbf { j }$
D) $\mathbf { r } ( \mathrm { t } ) = ( \tan \mathrm { t } ) \mathbf { i } + \left( \mathrm { t } ^ { 4 } - 6 \mathrm { t } - 4 \right) \mathbf { j }$