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Systems of Differential Equations
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Consider the system of differential equations (\frac{dx}{dt} = 2x - y, \ \frac{dy}{dt} = x + 2y). Find the eigenvalues of the coefficient matrix.
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A
(\lambda_1 = 1, \lambda_2 = 3)
💡 Explanation:
The eigenvalues are found by solving the characteristic equation (\det(A - \lambda I) = 0), where (A) is the coefficient matrix. Solving this equation gives ((\lambda - 1)(\lambda - 3) = 0), which has eigenvalues (\lambda_1 = 1) and (\lambda_2 = 3).