A jar contains 100 mL of a certain substance which, when heated to tt degrees Celsius contains E(t) = 2.3 t^2 - 4.5E(t)=2.3t2−4.5 Joules of thermal energy. Assuming that the thermometer measuring the temperature of the substance is accurate to within 0.20.2 degrees Celsius. Find \displaystyle \frac{dE}{dt}dtdE​ first, and then use differentials to estimate the possible error in the calculated thermal energy at t = 60t=60 degrees.

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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.