Math Problem Statement

What type of solutions does the following set of differential equations have? dx/dt = -2x, dy/dt = -8x-6y (a) x and y both tend monotonically to zero (b) x and y oscillate and the oscillations become larger with time (c) x and y oscillate and the oscillations become smaller with time (d) x and y both tend monotonically to infinity

Solution

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Math Problem Analysis

Mathematical Concepts

Differential Equations
Systems of Equations
Stability Analysis

Formulas

dx/dt = -2x
dy/dt = -8x - 6y

Theorems

Stability of Equilibrium Points
Linearization

Suitable Grade Level

Grades 11-12

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