Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) r(0) 2, y(0)1 Determine the nullclines, sketch the vector field, and then...
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) 1. (0)1, y(0)0 Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) 1. (0)1, y(0)0
PPLEASE SOLVE NUMBER 6 ONLY Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2 Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe" 1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only for x,y 20. x' = x(y + 2x-2), y' = y(y-1 ) (a) 1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only for...
1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only for x,y 20. (b) x' = x(y + 2x-2), y' = y(y + x-3) 1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only...
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2) Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Problem 13 15pts Carefully sketch the vector field vf(z, y) using at least 25 points if Problem 14 Demonstrate that the vector field is or is not con.servative. Problem 15 25pts Find a vector field n(u, v) of unit normals to r(u,)(2cos(u)sin(), 3sin(u)sin(v), cos(v) Problem 13 15pts Carefully sketch the vector field vf(z, y) using at least 25 points if Problem 14 Demonstrate that the vector field is or is not con.servative. Problem 15 25pts Find a vector field n(u,...
Sketch the slope field of y' = ty to determine lim --- y(t) such that y is a solution with y(0) < 0. The limit is 00 -00 -1
all a,b,c,d 1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on C with gradient Vg, we define the normal derivative Dng by and we define the Laplacian, V2g, of g by For this problem, assume D and C satisfy the hypotheses of Green's Theorem and the appropriate partial derivatives of f...