# differential equation: Show that if f and f' are continuous on a ≤ x ≤ b then f and f' are linearly independent on a ≤ x ≤ b

Show that if f and f' are continuous on a ≤ x ≤ b and f(x) is not zero for all x on a ≤ x ≤ b,
then f and xf are linearly independent on a ≤ x ≤ b.

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