Answered: Given the system: dx/dt=x+ 6y,…

Given the system: dx/dt=x+ 6y, dy/dt=−x+y (a) Find the general solution. (b) Find the solution that satisfies the initial condition (x(0), y(0)) = (2,1). Report your solution as one vector.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Given the system:

dx/dt=x+ 6y,

dy/dt=−x+y

(a) Find the general solution.

(b) Find the solution that satisfies the initial condition (x(0), y(0)) = (2,1). Report your solution as one vector.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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