Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Characteristic Equation
Complex Roots
Second-Order Linear Differential Equations
Formulas
Characteristic equation: r^2 - 4r + 29 = 0
Quadratic formula: r = (-b ± √(b^2 - 4ac)) / 2a
General solution for complex roots: y(t) = e^(αt)(c1 cos(βt) + c2 sin(βt))
Theorems
Solution to homogeneous linear differential equations with constant coefficients
Quadratic formula
Suitable Grade Level
Undergraduate Mathematics
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