Question: The autonomous differential equation with x(0) = l. This describes a population with per capita production that decreases like 1/1 + x 2 . Describe
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.
dx dt 1+x?
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