When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV1.4 = C where C is a constant. Suppose that at a certain instant the volume is 540 cm , and the pressure is 99 kPa (kPa = kiloPascals) and is decreasing at a rate of 12 kPa/minute. At what rate is the volume increasing at this instant? The volume is increasing at cm /min.

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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.