(Solved): Solve the initial value problem. Find the solution of the given initial value problem. Determine t ...

Solve the initial value problem. Find the solution of the given initial value problem. Determine the behavior of the solution as \( t \rightarrow \infty \). \[ y^{\prime \prime}+12 y^{\prime}=0, y(0)=-5, y^{\prime}(0)=12 \] \[ \begin{array}{l} y=-4+e^{-12 t}, \quad \lim _{t \rightarrow \infty} y(t)=-4 \\ y=4+e^{-12 t}, \quad \lim _{t \rightarrow \infty} y(t)=4 \\ y=4-e^{-12 t}, \quad \lim _{t \rightarrow \infty} y(t)=4 \\ y=-4-e^{-12 t}, \quad \lim _{t \rightarrow \infty} y(t)=-4 \\ y=4+e^{12 t}, \quad \lim _{t \rightarrow \infty} y(t)=\infty \end{array} \]