1) Solve a( 4 - 4x72x + x24 = 0 using the integrating factor 1= d 2) solve: 4" - H4 + 34 = 20 cox 10 using the undetermined coefficients method 3 ) solve : y" - Hq + 44 = 4coat; 410)=2, 410)-5 using Laplace transform4) solve the homogeneous system (25 pts ) = HX +54 dy = -4X - 44 a ) find the characteristic equation b) solve for the eigenvalues (J solve for one eigenvector aJ write the eigenvectoras a sum of 2 vectors ( e.g., read part + (maginary part) el Determine the 2 solutions of the system in matrix form () write out the general solution of the system as a linear combination of the 2 solutions.5) solve the non-homogeneous system using the undetermined coefficients method thod (35 pts ) x = AX+ 34 + 2et di - 9x+64+ 10e a) write the system in mate form 6) solve the associated homogeneous system " Determine the form of the particular solution Cyp) d ) solve for the particular solution. e write the general solution in matrix form