Forcing

We define two functions, $f(t)$ and $g(t)$, to be linearly independent on an open interval $I = (a, b)$ if there do not exist nonzero constants $c_1$ and $c_2$ such that for all $t \in I$. Equivalently, two functions are linearly independent, if one function is not a multiple of the other. Otherwise, $f(t)$ and $f(t)$ are linearly dependent. Suppose that $f(t)$ and $g(t)$ are solutions to the homogeneous linear equation Show that $f(t)$ and $g(t)$ are linearly…