Math Problem Statement
dx/dt=2x-8y, dy/dt=x+6y with x(0)=4, y(0)=1 solve
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Eigenvalue Problems
Linear Algebra
Formulas
dx/dt = 2x - 8y
dy/dt = x + 6y
Matrix representation: d/dt [x(t); y(t)] = A [x(t); y(t)]
Eigenvalue equation: det(A - λI) = 0
Euler's formula: e^(iθ) = cos(θ) + i sin(θ)
Theorems
Eigenvalue and Eigenvector Theorem
Euler’s Formula
Diagonalization of Matrices
Suitable Grade Level
Undergraduate Mathematics
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