Sketch phase portraits for the following linear systems: (a) x = 0, y = x

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Sketch phase portraits for the following linear systems:

(a) ˙ x = 0, ˙ y = x + 2y;

(b) ˙ x = x + 2y, ˙ y = 0;

(c) ˙ x = 3x + 4y, ˙ y = 4x − 3y;

(d) ˙ x = 3x + y, ˙ y = −x + 3y;

(e) ˙ x = y, ˙ y = −x − 2y;

(f) ˙ x = x − y, ˙ y = y − x.

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