A vat initially contains 120 L of syrup

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A vat initially contains 120 L of syrup. Let

y(t)

be the kilograms of sugar in the vat

t

minutes after pumping begins. Fresh syrup containing 0.10 kg of sugar per liter flows in at a rate of

4+2\cos t

L/min, while the mixture is withdrawn at a rate of

0.05\,y(t)

kg/min. Derive a differential equation that models

y(t)