Ordinary differential equations

Hi there. Well, I have some doubts about this exercise, I think I've solved it, but I wanted your opinion, which always help. So, it says:

There is no general method for solving the homogeneous general equation of second order

(1)

But if we already know a solution , then we always can find a second solution linearly independent

Demonstrate that this functions form a basis for the space of solutions of the differential equation (1).

So, what I did is simple. I know that if the solution is linearly independent, then the Wronskian must be zero. So, I just made the calculus for the wronskian:

Is this right?

Bye there.