# Wronskian computation

• May 12th 2008, 03:35 PM
Jim Newt
Wronskian computation
Given set of functions: 1, x, x^2, x in any interval; compute the Wronskian of this given set of functions and then determine whether the function is linearly dependent or independent. Could someone explain how to go about this? Thanks,

Jim
• May 13th 2008, 12:58 PM
flyingsquirrel
Hi

For three functions $f_1,\,f_2,\,f_3$, the wronskian is $W(x)=\left| \begin{array}{ccc}
f_1(x) & f_2(x) & f_3(x)\\
f_1'(x) & f_2'(x) & f_3'(x)\\
f_1''(x) & f_2''(x) & f_3''(x)
\end{array}
\right|$
and the functions are linearly independent if the wronskian is nonzero.