Unit 7: Differential Equations

Find the solution to [math] with [math].

The solution to the differential equation [math] with [math] is

If [math] and [math] and [math], then [math]

Using Euler's method with step size [math], starting at [math], the approximate value of [math] for [math] is

The logistic differential equation [math] has a carrying capacity of

Which slope field corresponds to the differential equation [math]?

The general solution of [math] for [math] is

Solve [math] with [math].

Use Euler's method with step size [math] to approximate [math] given [math] and [math].

On a slope field for [math], what is the slope at the point [math]?

The population [math] satisfies [math]. What is the carrying capacity?

Which equation is separable?

Solve [math] with [math].

At what value of [math] does [math] grow fastest?

What family of curves has [math]?

The logistic differential equation [math] models a population. At what value of [math] is the rate of growth the greatest?

The particular solution to [math] with initial condition [math] is