Linear independant or dependant?

Yes, you have the zero function, so the given set of functions is linearly dependent, no matter what other functions are.

In general, to check whether a given set of functions are linearly independent or dependent, look at the Wronskian:

\(\displaystyle \L W(x) =
\left|
\begin{matrix}
f_1 & f_2 & f_3 \\
f_1^\prime & f_2^\prime & f_3^\prime \\
f_1^{\prime \prime} & f_2^{\prime \prime} & f_3^{\prime \prime}
\end{matrix}
\right|\)

If W(x)=0 for all x, then the functions are linearly dependent, otherwise independent.
 
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