I am stuck on this math problem:  Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature. In the book, I got the differential equation of Newton's Cooling which is dT/dt = k(A-T). T is the temperature, A is the ambient temperature, t is the time in minutes, k is a constant. By separating the variables and integrating both sides, I got T= A + e^c * e^kt. I tried to solve for A using the available values, but can't seem to solve for A.

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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.