Hello. Please answer the following question, ensure that your answer is correct and supported by calculations, explanations and algebraic work. Only utilize the sections/topics seen below. Solutions for Ordinary Differential Equations must be given in real values form(i.e. no complex or imaginary values). Please organize your work, in a reasonably neat and coherent way. Thank you so much, I hope you have a great day!

Topics: first order linear (autonomous) systems linear systems II (like phase planes and direction fields) linear systems III(like eigenvalues and eigenvectors) linear systems IV (like rewriting undamped oscillators as a system, using eyelets principle and linearity principle, classification of equilibrium point Linear systems V (eigenvalues, trace of a matrix) Systems (evecs)

Solve the following initial-value problem; give the solution in vector form. dY 6 -1 4 Y, Y (0 ) = dt 5 4 -2