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## Homework Statement

If two differentiable functions are linearly dependent on the interval I, then their Wronskian is identically zero on I.

## Homework Equations

## The Attempt at a Solution

We start with the definition of linearly dependence for two functions.

##y_1 = Cy_2##

##\displaystyle \frac{y_1}{y_2} = C##

##\displaystyle \left( \frac{y_1}{y_2} \right)' = 0##

##\displaystyle \left( \frac{y_1}{y_2} \right)' = \frac{y_1' y_2 - y_2' y_1}{y_2^2}= 0##

##\displaystyle y_1 y_2' - y_2 y_1'= 0##

This seems fine, but how can I justify my second step? How can I divide by ##y_2## without knowing if ##y_2## is zero somewhere on the interval I?