]1. The problem statement, all variables and given/known data Trying to get a good start on a second order, non-homogeneous, linear differential equation with constant coefficients. The differential equation is y”-4y’+4y=(1+x+x2+x3)e2x y(0)=1; y’(0)=0 The constraints with this problem is that I cannot use Laplace transform to solve the problem. So, I am looking at all the ways I can solve this mess of a problem. I only know of two ways to ways to approach a second order, non-homogenous problem and that is by “undetermined coefficients” and “variation of parameters.” 2. Relevant equations I only know of two ways to ways to approach a second order, non-homogenous problem and that is by “undetermined coefficients” and “variation of parameters.” 3. The attempt at a solution Out of all the reading I have done, I only two methods on how to approach this problem, I am still running into a hard time getting it started. I am not even sure if using variation of parameters is the correct and most efficient method? But when I break it down using variation of parameters, I get: y”-4y’+4y → λ2-4λ+4=0 → λ=2 so yh(x)=Ce2x. Even if this is right, I don’t know what to do with the right side of the equation. When I look at the “undetermined coefficients” method I think I can divide both sides by e2x but then it gets kind of nasty from there. Am I even on the right track with either of these methods and if not can someone head me in the right directio? Remember: I cannot solve this equation by using the Laplace transform, it is part of the constraints to the problem.