The autonomous differential equation with x(0) l This describes a population with per capita production that decreases like 1 1 x 2 Describe in words how the solution differs from that in Exercise 15 The following autonomous differential equations can be solved except for the step of finding x in t...

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The autonomous differential equation with x(0) = l. This describes a population with per capita production that

Question:

The autonomous differential equation

with x(0) = l. This describes a population with per capita production that decreases like 1/1 + x².Describe in words how the solution differs from that in Exercise 15.

The following autonomous differential equations can be solved except for the step of finding x in terms of t. Use the steps to figure out how the solution behaves.

a. Solve the equation with separation of variables.

b. It is impossible to algebraically solve for x in terms of However, you can still find the arbitrary constant. Find it.

c. Although you cannot find x as a function of t, you can find t as a function of x. Graph this function for 1 ≤ x ≤ 10.