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An example of modeling a real-world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball's velocity. This means that the ball's acceleration, which is a derivative of its velocity, depends on the velocity (and the velocity depends on time). Finding the velocity as a function of time involves solving a differential equation and verifying its validity.
An example of modeling a real-world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball's velocity. This means that the ball's acceleration, which is a derivative of its velocity, depends on the velocity (and the velocity depends on time). Finding the velocity as a function of time involves solving a differential equation and verifying its validity.
使用微分方程模拟现实世界问题的一个例子是仅考虑重力和空气阻力确定球在空中落下的速度。球对地面的加速度是由于重力加速度减去由于空气阻力提供的加速度。重力被认为是常数，空气阻力可以被模拟为与球的速度成正比。这意味着球的加速度，也就是其速度的导数，取决于速度(而速度取决于时间)。找到时间的函数--速度--需要解决一个微分方程问题并验证它的有效性。
==Types==
==Types==