Basically, the title says it all, I need to figure out whether these functions are linearly independtend on (-infinity, infinity)
Wronskian (the determinant of the matrix composed of the functions in the first row, first derivative in the second row and second derivatives in the third row)
The Attempt at a Solution
After computing the Wronskian this is what I got:
[(-e^-x)(-cosx)] + [(xe^-x)(-sinx)] - [(x)(-e^-x)(cosx)] - [(e^-x)(cosx)]
however, I cannot seem to simply this. If anyone can help me simplify this further that would be great. Also if you help me determine if whether they are linearly independent.