The importance of the Wronskian
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Determine whether the following functions can be Wronskians on -1<x<1 for a pair of solutions to some equation y''+py'+qy = 0 with p and q continuous.
a) W(x) = 6e^4x
b) W(x) = x^3
c) W(x) = 0
d) W(x) = (x-1/2)^2
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The solution demonstrates the information about the solutions of the differential equations using the Wronskian.