Solve the differential equation using the method of undetermined coefficients. 
Definitions:
Previous Friendships
Relationships of mutual affection with individuals whom one has been friends with in the past.
Long-term Partnership
A committed relationship between two individuals that is intended to last a significant amount of time, often involving cohabitation or marriage.
Crucial Aspect
An essential element or feature of something.
Remarriage
The act of marrying again after a divorce or the death of a spouse, involving entering into a new marital relationship.
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