Question 16. Consider the following system of differential equation: 2 = 52 ty ý = 5y - x (a) Find the eigenvalues and eigenvectors associated with this system. (b) Write down the general solution formula for the system. (c) Give the particular soluton for the initial values x(0) = 0, y(0) = 1. du pullalines in the phase plane.

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Chapter2: Second-order Linear Odes
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Question 16.
Consider the following system of differential equation:
2 = 52 +y
ý =5y - x
(a) Find the eigenvalues and eigenvectors associated with this system.
(b) Write down the general solution formula for the system.
(c) Give the particular soluton for the initial values x(0) = 0, y(0) = 1.
(d) Draw the x- and y-nullclines in the phase plane.
(e) Sketch the solution curve for the initial condition in part (c) in the phase plane.
(f) Is the point (0,0) stable or unstable? Classify this equilibrium.
15-1)(1-A)- 5
Transcribed Image Text:Question 16. Consider the following system of differential equation: 2 = 52 +y ý =5y - x (a) Find the eigenvalues and eigenvectors associated with this system. (b) Write down the general solution formula for the system. (c) Give the particular soluton for the initial values x(0) = 0, y(0) = 1. (d) Draw the x- and y-nullclines in the phase plane. (e) Sketch the solution curve for the initial condition in part (c) in the phase plane. (f) Is the point (0,0) stable or unstable? Classify this equilibrium. 15-1)(1-A)- 5
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