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# First Order Differential Equations

These are equations, Calculus-style. From modeling real-world phenomenon, from the path of a rocket to the cooling of a physical object, Differential Equations are all around us.

# Differential Equations - Formulate a Statement

Suppose that we drop a stone, which falls freely with no air resistance. Experiments show that, under that assumption of negligible air resistance, the acceleration $${y}^{\prime\prime}=\frac { {d}^{2}y }{ {d}^{2}t }$$ of this motion is constant, i.e. equal to the so-called acceleration of gravity $$g=9.8 \text{ m/sec}^2.$$ State this as an ordinary differential equation for $$y(t),$$ the distance fallen as a function of time $$t.$$

Because of limited food and space, a squirrel population cannot exceed $$2900$$ squirrels. The population grows at a rate proportional to the product of the existing population and the attainable additional population. If $$P$$ denotes the squirrel population at time $$t,$$ which of the following equations represents the population growth rate for $$k>0?$$

In psychology, a stimulus-response situation is a situation in which the response $$y=f(x)$$ changes at a rate inversely proportional to the strength of the stimulus $$x$$. Which of the following equations represents this?

For a body moving along a straight line, let $$y(t)$$ denote its distance from a fixed point $$O$$ at time $$t.$$ Given that velocity plus distance is equal to square of time, find the ordinary differential equation of the motion.

Jack has a magic beanstalk, whose rate of growth is directly proportional to its height $$H$$. Which of the following equations represents his beanstalk's height as a function of time $$t$$?

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