To determine Calculate the vector r from the given initial value problem. Explanation Given information: Consider that the differential equation. d r d t = 3 2 ( t + 1 ) 1 / 2 i + e − t j + 1 t + 1 k (1) Consider that the initial condition. r ( 0 ) = k (2) Calculation: Integrate both sides of Equation (1) to find the vector r . ∫ d r d t = ∫ ( 3 2 ( t + 1 ) 1 / 2 i + e − t j + 1 t + 1 k ) d t = [ 3 2 ( t + 1 ) 3 / 2 3 2 ] i + [ − e − t ] j + [ ln ( t + 1 ) ] k + C { ∵ ∫ t n d t = t n + 1 n + 1 } r = [ ( t + 1 ) 3 / 2 ] i + [ − e − t ] j + [ ln ( t + 1 ) ] k + C (3) Substitute 0 for t in Equation (3)

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Chapter 13.2, Problem 13E

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Calculate the vector r from the given initial value problem.

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