Solve the differential equation using the method of undetermined coefficients. 
Definitions:
Marginal Product Data
Information that shows the additional output generated by adding one more unit of a factor of production, holding all else constant.
Purely Competitive Market
A market structure characterized by a large number of buyers and sellers, homogeneous products, and no barriers to entry or exit, which leads to competitive pricing.
Maximize Profits
The goal of firms to achieve the highest possible profit by adjusting production and pricing strategies.
Marginal Product Data
Information related to the additional output generated by employing one more unit of a particular input.
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