Consider the following second order linear ODE y" - 5y +6y=0, where y' and y" are first and second order derivatives with respect to . (a) Write this as a system of two first order ODEs and then write this system in matrix form. (b) Find the eigenvalues and eigenvectors of the system. (c) Write down the general solution to the second order ODE. (d) Using your result from part 3 (or otherwise) find the solution to the following equation. y' - 5y +6y=3e^2x
