Consider the system of differential equationsd.x= x + 4ydtdy2x – ydt(i) Write the system (E) in a matrix form.(ii) Find a vector solution by eigenvalues/eigenvectors.(iii) Use the vector solution, write the solutions x(t) and y(t).

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Answered: Consider the system of differential…

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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Consider the system of differential equations dx = x + 4y dt (Σ) dy 2x – y dt (i) Write the system (E) in a matrix form. (ii) Find a vector solution by eigenvalues/eigenvectors. (iii) Use the vector solution, write the solutions x(t) and y(t).