Question: Please help me with this study question and show work. It has three parts but it's the same problem. THANKS! Consider the differential equation for

Please help me with this study question and show work. It has three parts but it's the same problem. THANKS!

Consider the differential equation for x[ t) x\" + 2x' + 5x = 5. (a) Construct the homogeneous solution for this differential equation. (b) Construct a particular solution. (c) Construct the solution that satisfies x{) = D and x'(0) = 1

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