Solve the Initial Value Problem Initial Condition $\mathbf { r } ( 0 ) = 5 \mathbf { i } - 6 \mathbf { j }$

question 69

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = \left( \mathrm { t } ^ { 4 } + 5 \mathrm { t } ^ { 2 } \right) \mathbf { i } + 4 \mathrm { t } \mathbf { j }$
Initial Condition: $\mathbf { r } ( 0 ) = 5 \mathbf { i } - 6 \mathbf { j }$

• A) \(r ( t ) = \left( \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } - 6 \right) i + \left( 2 t ^ { 2 } + 5 \right) \mathbf { j }\)
• B) \(\mathbf { r } ( \mathrm { t } ) = \left( \frac { \mathrm { t } ^ { 5 } } { 5 } + \frac { 5 \mathrm { t } ^ { 3 } } { 3 } \right) \mathbf { i } + 2 \mathrm { t } ^ { 2 } \mathbf { j }\)
• C) \(r ( t ) = \left( \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } + 5 \right) i + \left( 2 t ^ { 2 } - 6 \right) \mathbf { j }\)
• D) \(r ( t ) = \left\{ \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } + 5 \right) i + \left( t ^ { 2 } - 6 \right) j\)

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