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The slope field for the system dx dt = 2x + 1 2 y dy dt =

Chapter , Problem 19

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QUESTION:

The slope field for the system dx dt = 2x + 1 2 y dy dt = y is shown to the right. (a) Determine the type of the equilibrium point at the origin. (b) Calculate all straight-line solutions. (c) Plot the x(t)- and y(t)-graphs, (t 0), for the initial conditions A = (2, 1), B = (1, 2), C = (2, 2), and D = (2, 0).

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QUESTION:

The slope field for the system dx dt = 2x + 1 2 y dy dt = y is shown to the right. (a) Determine the type of the equilibrium point at the origin. (b) Calculate all straight-line solutions. (c) Plot the x(t)- and y(t)-graphs, (t 0), for the initial conditions A = (2, 1), B = (1, 2), C = (2, 2), and D = (2, 0).

ANSWER:

Step 1 of 7

a)

Consider the linear system,

The system can be written as,

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