Solve the differential equation using the method of undetermined coefficients. 
Definitions:
Conversion Ratio
The specific quantity of one asset or liability that can be exchanged for another, often used in the context of convertible securities.
Risk-free Rate
The estimated rate of profit for a no-risk investment, usually depicted by the earnings from government securities.
American Call
An option contract that gives the holder the right to buy a specific asset at a set price anytime before the expiration date.
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