Question: Make sure to discuss the reason for your conclusion from a to d please Do the following two problems: 1) Consider the nonhomogeneous 2 d

Make sure to discuss the reason for your conclusion from a to d please

Do the following two problems: 1) Consider the nonhomogeneous 2 d order differential equation y" + 2y' = x. a) Algebraically investigate the existence of a quadratic solution to the equation. That is, substitute y, = ax + bx+ c into the equation. Is such a solution possible? Discuss the reasoning for your conclusions. b) Now find the complementary function, y , representing the general solution to the associated homogeneous DE. Explain how this y, may shed light on your conclusions in part a). c) Amend the form of y, from part a) and substitute it back into the differential equation to determine the necessary values for the coefficients a, b, and c to yield a solution. d) Finally, knowing y, and yo , write the general solution to the differential equation

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