Solve the Initial Value Problem Initial Condition $\mathbf { r } ( 0 ) = 9 \mathrm { i } + \frac { 55 } { 14 } \mathrm { j } - 6 \mathbf { k }$

question 123

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = ( 3 \sec 3 \mathrm { t } \tan 3 \mathrm { t } ) \mathrm { i } + \frac { \mathrm { t } } { \left( \mathrm { t } ^ { 2 } + 7 \right) ^ { 2 } } \mathrm { j } + \mathrm { t } ^ { 2 } \mathbf { k }$
Initial Condition: $\mathbf { r } ( 0 ) = 9 \mathrm { i } + \frac { 55 } { 14 } \mathrm { j } - 6 \mathbf { k }$

• A) \(\mathbf { r } ( t ) = ( \sec 3 t + 8 ) \mathbf { i } - \frac { 1 } { 2 t ^ { 2 } + 14 } \mathbf { j } + \left( \frac { t ^ { 3 } } { 3 } - 6 \right) \mathbf { k }\)
• B) \(r ( t ) = ( \csc 3 t + 8 ) \mathbf { i } + \left( 4 - \frac { 1 } { 2 t ^ { 2 } + 14 } \right) j \mathbf { j } + \left( t ^ { 3 } - 6 \right) \mathbf { k }\)
• C) \(\mathbf { r } ( \mathrm { t } ) = ( \csc 3 \mathrm { t } + 8 ) \mathbf { i } + \left( 4 - \frac { 1 } { 2 \mathrm { t } ^ { 2 } + 14 } \right) \mathbf { j } + \left( \frac { \mathrm { t } ^ { 3 } } { 3 } - 6 \right) \mathbf { k }\)
• D) \(r ( t ) = ( \sec 3 t + 8 ) i + \left( 4 - \frac { 1 } { 2 t ^ { 2 } + 14 } \right) j \mathbf { j } + \left( \frac { t ^ { 3 } } { 3 } - 6 \right) \mathbf { k }\)