"[Here] we explore a relationship between determinants and solutions to a differential equation. The matrix consisting of solutions to a differential equation and their derivatives is called the Wronskian and, as we will see in later chapters, plays a pivotal role in the theory of differential equations."
This is the question following the description:
"Verify that are solutions to the differential equation: , and show that is nonzero on any interval."
Now I'm really just looking for an explanation on how I would show that it is nonzero on any interval. I completed the first part, I believe, by just taking up to the third derivative for each and plugging each set in to verify an identity of 0=0 at the end. I would then put the terms into the matrix which would give me:
So I've gotten this far and if anyone could point me in the right direction on where to go from here it would be greatly appreciated.