Vector field / phase portrait

Slope fields, phase portraits, equilibria. Help

x'' = −x written as a system: let y = x' (the velocity), so x' = y, y' = −x. The origin is a center (linearization can only say 'center or weak spiral'); the orbits are the circles x² + y² = C, that is x² + x'² = C.
Parameters

Write a letter in the equation (the k in k*y) and it appears here with a value you can change.

Show on the picture
Initial value
Query the solution
View

Phase plane — horizontal x, vertical y

x ∈ [-4.17, 4.17], y ∈ [-3, 3] (equal scale)

Results for x ∈ [-3, 3], y ∈ [-3, 3]

Equilibria

  1. (0, 0) center or weak spiral (linearization cannot tell) λ = ±1i · tr = 0, det = 1

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