Hospital patients are often given glucose (blood sugar) through a tube connected to a bottle suspended over their beds. Suppose that this "drip" supplies glucose at the rate of 30 mg per minute, and each minute 25% of the accumulated glucose is consumed by the body. Then the amount y(t) of glucose (in excess of the normal level) in the body after t minutes satisfies the following. y'  =  30 − 0.25y    (Do you see why?) y(0)  =  0    (zero excess glucose at t = 0) Solve this differential equation and initial condition. y(t) = ?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.