Coupled Differential Equations flashcards

8 practice cards drawn from the Coupled Differential Equations lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.

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What makes a pair of differential equations coupled?

each rate depends on both quantities

from “Coupled Differential Equations”

dx/dt = x + y and dy/dt = 4x + y. Where does the pair stay still?

at the origin

from “Coupled Differential Equations”

M has eigenvalues 3 and −1 with eigenvectors (1, 2) and (1, −2). The general solution is

A e^(3t)(1, 2) + B e^(−t)(1, −2)

from “Solving a Coupled System with Eigenvalues”

Feeding X = e^(λt) v into dX/dt = M X requires

M v = λ v

from “Solving a Coupled System with Eigenvalues”

The eigenvalues are −1 + 2i and −1 − 2i. The paths

spiral into the origin

from “Phase Portraits and Equilibrium Types”

The eigenvalues are −2 and −4. The origin is

a stable node

from “Phase Portraits and Equilibrium Types”

To turn x″ + 3x' + 2x = 0 into a pair, what is named v?

dx/dt

from “A Second-Order Equation as a Coupled System”

The characteristic polynomial of that M is

λ² + 3λ + 2

from “A Second-Order Equation as a Coupled System”

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