Solve the differential equation using the method of undetermined coefficients. 
Definitions:
Achievement
The process of accomplishing a task or goal, often of significant difficulty, through effort, skill, or courage.
Achievement Motive
The internal drive or aspiration to accomplish tasks and goals, often leading to success and personal satisfaction.
Being Admired
The feeling or state of being regarded with respect or warm approval.
Outperforming Others
Outperforming others refers to achieving better results or performance in comparison to peers or competitors, often used in educational, professional, or athletic contexts.
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