Determine two functions defined on the interval infinity inf

Determine two functions, defined on the interval (-infinity, infinity), whose Wronskian is given by W (f_1, f_2) = e^2x. Are the functions that you found linearly independent on (-infinity, infinity)? How do you know?

Solution

The two funcitons are linearly independent if the Wronskian is non-zero in the given interval.

Since e^2x cannot be equal to zero for any x in given interval, so the given functions are linearly independent.