Need help with dicussion HW for Advanced Math

Advance Math

1. Please explain how we can convert an n-order ODE to a system of ODE's. What do we accomplish by this and what are the advantages?

2. Please search the internet or your textbook to find engineering problems resulting into a system of equations.

3. Please state here the definition of coupled DE's? Please state here the definition of coupled DE's?

4. what are some of the methods to solve this differential equation? Could you also explain how we can obtain eigenvalues of a matrix?