Calculate the Wronskian of each of the following sets of functions and determine

Question

Calculate the Wronskian of each of the following sets of functions and determine the conditions necessary for the Wronskian to be non-zero, i.e. the conditions necessary for the functions to be linearly independent. Assume alpha, beta and gamma as well as m and n are constants where applicable. f1(x) = a cos bx and f2(x) = ax cos bx. f1(x) = axr and f2(x) = bxs. f1(x) = eax and f2(x) = xe-ax. f1(x) = eax and f2(x) = ebx. If f1(x) = eax, f2(x) = ebx and f3(x) = ecx. Hint: Try using a TI-89 or similar calculator or other CAS system/program to factor the end result of the Wronskian determinant.

Explanation / Answer

W(f,g) = fg?

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