Write the linear system of differential equations in matrix form then solve the system.
dx/dt = x + y
dy/dt = 4x + y
x(0) = 1, y(0) = 2

In matrix form, the system is

First find the eigenvalues of the coefficient matrix (call it ).

Find the corresponding eigenvector for each eigenvalue:

Then the system has general solution

or

Given that and , we have

so that the system has particular solution

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step-by-step explanation: