Math Problem Statement
y''+4y'+5y=0
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Second-Order Linear Homogeneous Equations
Complex Numbers
Oscillatory Behavior
Formulas
y'' + 4y' + 5y = 0
General solution: y(t) = e^{rt}
Characteristic equation: r^2 + 4r + 5 = 0
Quadratic formula: r = (-b ± sqrt(b^2 - 4ac)) / 2a
Complex solution: y(t) = e^{-2t} (C_1 cos(t) + C_2 sin(t))
Theorems
Quadratic Formula
General Solution for Complex Roots in Differential Equations
Suitable Grade Level
Undergraduate level (Calculus II or Differential Equations)
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