Question: Consider the differential equation y - 6y' + 9y= 4xe3x + 7 sin(3x) (a) Give the associated homogeneous linear differential equation. (b) Determine the

Consider the differential equation y\

Consider the differential equation y" - 6y' + 9y= 4xe3x + 7 sin(3x) (a) Give the associated homogeneous linear differential equation. (b) Determine the characteristic equation of y" 6y' + 9y = 0. (c) Identify two linear independent solutions of (2). (d) Write the general solution of (2). (e) Determine the solution of (2) that satisfies y(0) = 1 and y'(0) = 0. (f) Find the FORM of a particular solution of 3x y" 6y' + 9y = 4xe (g) Find the FORM of a particular solution of y" 6y' + 9y = 7 sin(3x). (h) What is the FORM of a particular solution of 3x y 6y' + 9y = 4xex + 7 sin(3x). (2)

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