Autonomous Equations Recall that if the right-hand side is independent of variable t, so that the DE has the form y = f(y), the equation is called autonomous. (See Problem 61 in Sec. 1.2.) Such equations are always separable.
(a) Identify the autonomous equations in Problems.
(b) How can you recognize the direction field of an autonomous equation?
Find the autonomous equations. See how this property shows up in the direction fields and solutions. (For comparison, all 12 IDE pictures are printed out in Lab 2, Sec. 5.)
Problem 61 in Sec. 1.2
Autonomous Equations
When a first-order DE has the form y' = f(y), so the right-hand side doesn’t depend on t, the equation is called autonomous (which means independent of time).
The logistic equation y' = ky(1 − y) in Problem 60 and the equation y' = y2− 4 in Example 9 are examples of autonomous equations.
(a) List those DEs in Problems 9-17 and 31–39 that are autonomous.
(b) What is the distinguishing property of isoclines for autonomous equations?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.