Could anyone please solve this for me? Sorry to ask that, im in great need and just couldnt do it myself...
I am former University professor, so it would inappropriate for me just to give you the solution, but I can provide explanation which would be sufficient for you (of course, if you work hard yourself) to solve the problem. First, you have to look at the definition of conservative force and one of such definitions implies that force should be a function of coordinates only. So, if you see force depending on velocity or time, such force if not conservative.
If force is conservative, then f_x will be equal to minus derivative of potential function with respect to x and f_y will be equal to minus derivative of potential function with respect to y. This means that derivative of f_x with respect to y should be equal to derivative of f_y with respect to x. Try the example 3, 4, and 5 and let me know what your conclusion. If those derivatives are not equal one to another, the forces are not conservative. If those derivatives are equal, you can find potential function and setting this function to a constant would give you a conservation law.