This is an example adapted from the textbook "Measurement and Instrumentation Principles from Alan S. Morris".
It shows the power of Matlab when working with Differential Equations, Laplace Transforms, and more, in a practical but not too difficult example for instrumentation engineers (Industrial, Mechánical, Manufacturing, among other).

This is the problem statement:
A balloon is outfitted with instruments that measure temperature and altitude, along with radio equipment to transmit these readings to the ground. Initially anchored, the balloon's instruments stabilize their output readings. The altitude instrument is approximately zero-order, while the temperature transducer is first-order with a 15-second time constant. The ground temperature (T0) is 10°C. The temperature (Tx) at an altitude of x meters is expressed as Tx = T0 - 0.01x, meaning the temperature drops by 0.01 degrees per meter.

Task:

Upon releasing the balloon, it ascends at 5 meters per second starting from time zero. Your task is to calculate the temperature readings measured by the instruments. Compare these readings with the actual temperature, analyze the differences, and draw conclusions from your analysis.