Find the solution of the system x' = -4x - 2y, y=-2x - 4y, where primes indicate derivatives with respect to t, that satisfies the initial condition (0) = 1, y(0) = -4. x = Based on the general solution from which you obtained your particular solution, complete the following two statements: The critical point (0,0) is A. unstable B. stable O C. asymptotically stable and is a(n) O A. saddle point O B. spiral C. center D. node

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the solution of the system
x' = -4x - 2y, y = -2x - 4y,
where primes indicate derivatives with respect to t, that satisfies the initial condition x(0) = 1, y(0) = −4.
x =
y =
Based on the general solution from which you obtained your particular solution, complete the following two statements:
The critical point (0,0) is
O A. unstable
B. stable
O c. asymptotically stable
and is a(n)
O A. saddle point
B. spiral
C. center
D. node
Transcribed Image Text:Find the solution of the system x' = -4x - 2y, y = -2x - 4y, where primes indicate derivatives with respect to t, that satisfies the initial condition x(0) = 1, y(0) = −4. x = y = Based on the general solution from which you obtained your particular solution, complete the following two statements: The critical point (0,0) is O A. unstable B. stable O c. asymptotically stable and is a(n) O A. saddle point B. spiral C. center D. node
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