The problem :

Show that the functions , and are linearly independent if

Solution :

I calculated the wronskian, and my final answer is:

Clearly,

The problem here is with

Since , the following numbers can't be zero:

Now, I stopped!

- b-a
- a-c
- c-b

How I can prove that the expression can't be zero so that wronskian will be non zero and hence the function are linearly independent?