Solve the differential equation using the method of undetermined coefficients. 
Definitions:
Hydrochloric Acid
A strong acidic solution of hydrogen chloride in water, found in the stomach, where it aids in digestion and sterilization of ingested food.
Lysozymes
Enzymes that damage bacterial cell walls by catalyzing the hydrolysis of 1,4-beta-linkages between N-acetylmuramic acid and N-acetyl-D-glucosamine, found in saliva, mucus, and tears.
Bile Acids
Steroid acids found predominantly in the bile of mammals, crucial for the digestion and absorption of fats and fat-soluble vitamins in the small intestine.
Metabolizing
The complex set of life-sustaining chemical transformations within the cells of living organisms, including processes such as digestion, energy production, and detoxification.
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