The least possible value of k ,

for which the following boundary value problem has a solution is:

\(y''(t) + 3y'(t) + ky(t) = 0, \quad t \in \mathbb{R}, \)

with the boundary conditions:

\(y(0) = 0, \quad y(2) = 0, \quad y\left(\frac{1}{2}\right) = 2 \).

Find the value of k ( accurate up to two decimal places)