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

question 96

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = \frac { 3 } { 2 } ( \mathrm { t } + 3 ) ^ { 1 / 2 } \mathbf { i } + \mathrm { e } ^ { \mathrm { t } } \mathbf { j }$
Initial Condition: $\mathbf { r } ( 0 ) = 0$

• A) \(r ( t ) = \left[ ( t + 3 ) ^ { 3 / 2 } - 3 ^ { 3 / 2 } \right] \mathbf { i } + \left( e ^ { t } - 1 \right) \mathbf { j }\)
• B) \(r ( t ) = \left[ ( t + 3 ) ^ { 5 / 2 } - 3 ^ { 5 / 2 } \right] \mathbf { i } + \left( e ^ { t } - 1 \right) \mathbf { j }\)
• C) \(\mathbf { r } ( \mathrm { t } ) = \left[ ( \mathrm { t } + 3 ) ^ { 3 / 2 } + 3 ^ { 3 / 2 } \right] \mathbf { i } + \left( \mathrm { e } ^ { \mathrm { t } } + 1 \right) \mathbf { j }\)
• D) \(\mathbf { r } ( \mathrm { t } ) = ( \mathrm { t } + 3 ) ^ { 3 / 2 } \mathbf { i } + \mathrm { e } _ { \mathbf { j } } \mathbf { j }\)

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Definitions:

Neuron

A specialized cell in the nervous system that transmits information to other nerve cells, muscle cells, or gland cells, primarily through electrical and chemical signals.

Glia

Supportive cells in the central nervous system that provide support and nutrition, maintain homeostasis, form myelin, and participate in signal transmission in the nervous system.

Neurons

Specialized neurons within the nervous system that convey information via electrical and chemical signals.

Dead Neurons

Neurons that have ceased to function and cannot transmit signals due to damage or disease.