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Find the function r that satisfies the given condition r'(t) = \left < e^t, - cos (t) , sec^2t...

Question:

Find the function {eq}r {/eq} that satisfies the given condition {eq}r'(t) = \left < e^t, - cos (t) , sec^2t \right >; r(0) = \left < 5,5,5 \right > {/eq}.

Initial Value Problem:

The initial value problem is solved using the integration method. We get an integration constant while integrating both sides of the equation, and we evaluate the constant value using the initial condition.

We substitute the constant value in the general solution to find the particular solution.

Answer and Explanation: 1

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Given Data: -

  • The given equation is: {eq}r'\left( t \right)= \left\langle {{e^t}, - \cos \left( t \right),{{\sec }^2}t} \right\rangle {/eq}
  • The...

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Initial Value in Calculus: Definition, Method & Example

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Chapter 11 / Lesson 13
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Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial value problems.


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