1. I have no idea how to solve this integral:
2. I've got two solutions from different sources to this DE, what is the difference and why they chose to write the solutions like that (how do I know when to write them as a product or as a sum)?
the equations is:
one solutions is:
and the other:
you need to solve the characteristic equation:
This has as a solution the four 4th roots of -1:
So the general solution is:
You may modify this form:
These two forms represent the most commonly used forms for this kind of solution.