Question

Solve the initial value problem: r' (t) = 3i + 3e'j + (3e' + 3te') k and r(0) = 5i + 3j + 3k

Answer 1

To solve the initial value problem r'(t) = 3i + 3e'j + (3e' + 3te')k and r(0) = 5i + 3j + 3k, you need to integrate each component of r'(t) separately and then substitute r(0) into the resulting equations.

Step-by-step explanation:

To solve the initial value problem r'(t) = 3i + 3e'j + (3e' + 3te')k and r(0) = 5i + 3j + 3k, you need to integrate each component of r'(t) separately and then substitute r(0) into the resulting equations. Let's start by integrating the i component:

1. Integrate 3i with respect to t:

∫(3i) dt = 3t + C1

Next, integrate the j component:

1. 
   
   Integrate 3e'j with respect to t:

∫(3e'j) dt = 3te' + C2