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In Problems 23–26 solve the given nonlinear plane autonomous system by changing to polar coordinates. Describe the geometric behavior of the solution that satisfies the given initial condition(s).
25.
[Hint: The resulting differential equation for r is a Bernoulli differential equation. See Section 2.5.]
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Chapter 10 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
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- x' = 1 х. Construct the phase plane for the points (2,2), (2,0), (2,-2), (0,2), (0,-2), (-2,2), (-2,0) and (-2,-2). 2.5 1.5 1 0.5 -0.5 -1 -1.5 -2 -2.5 3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2.5arrow_forward8. Find a vector b such that the system - (¹-1/²-3/2)x+b that could have the phase portrait shown below with a critical point at (1,1) 2 1.5 0.5 0 -0.5 -1 x'= -0.5 0 0.5 X 1 1.5 2arrow_forwardThis is the first part of a two-part problem. Let P = cos(6t) y(t) = |- (sin(6t)) | -6 sin(6t) , Y2(t) = -6 cos(6t) a. Show that y1 (t) is a solution to the system y = Py by evaluating derivatives and the matrix product (t) -6 0 Enter your answers in terms of the variable t b. Show that y2 (t) is a solution to the system y = Pj by evaluating derivatives and the matrix product y2(t) Enter your answers in terms of the variable t.arrow_forward
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