Let's consider the following nonhomogeneous first-order ODE: dy = dt 3.2y - 12t We first investigated how to solve such an ODE with the use of the Linearity Principle, which will be the focus of this question. a.) Find the solution, yh, to the homogeneous reduction. Be sure to show all work. b.) Craft an appropriate guess for y, and find the appropriate coefficient. Be sure to show all work. c.) Write the general solution to this ODE. d.) Suppose we replaced the -12t in the above ODE with 62t2. What would be an appropriate guess for yp? Do NOT solve for it... just tell me what the guess should be and why it is appropriate.

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