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The Wronskian is the determinant of the matrix of functions and their derivatives. For solutions of a linear ODE, a non-zero Wronskian anywhere proves linear independence and confirms a complete solution basis.
Wronskian
W(f₁, f₂) = f₁·f₂' − f₂·f₁'
W = 5 − 6 = −1, non-zero, so the two functions are independent at that point.
Not in general, but it does for solutions of the same linear ODE, thanks to Abel's identity.