# 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.