We consider the following second order differential equation: \mathrm{d}^{2} \mathrm{y} / \mathrm{dt}^{2}=5 \mathrm{dy} / \mathrm{dt}-4 \mathrm{y} . i) Write this equation as a system of two first order differential equations

of the form: \mathrm{d} / \mathrm{dt} \vec{x}=\mathrm{A} \cdot \bar{x} where \overrightarrow{\mathrm{X}}:=\left\langle\mathrm{X}_{1}, \mathrm{X}_{2}\right\rangle^{\top} and A is a 2x2 matrix. The matrix A is equal to: \text { ii) The eigenvalues } \lambda_{1}, \lambda_{2} \text { of the matrix } A \text { in ascending order }\left(\lambda_{1} \leq \lambda_{2}\right), \text { are equal to: } Write the corresponding eigenvectors (V1 corresponds to lambda1 and V2 corresponds to lambda2) in their simplest form, such as their first component is 1: The general solution of this second order differential equation has the form: The solution satisfying this second order differential equation and the initial conditions y(0)=0,dy/dt (0)=-27has: