In the theory of learning, the rate at which a subject is memorised is assumed to be proportional to the amount that is left to be memorised. However, the factor of forgetting influences the amount that have memorised. Thus, assume that the rate at which material is forgotten is proportional to the amount memorised at any time t > 0. Suppose M denotes the total amount of a subject to be memorised and A(t) is the amount memorised at time t > 0. Determine a differential equation for A(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.