Sketch the phase portrait of the scalar equation x x 6x 0

Sketch the phase portrait of the scalar equation x\'\' - x\' - 6x = 0 by converting to an equivalent system. Identify the origin and decide whether it is an attractor.

Solution

THE GOOD (1 solution) THE BAD (0 solution) THE UGLY ( solutions) \" 0 1 2 | 2 1 1 1 | 5 2 1 1 | 2 # \" 1 1 1 | 5 0 1 2 | 2 2 1 1 | 2 # \" 1 1 1 | 5 0 1 2 | 2 0 3 3 | 12 # \" 1 1 1 | 5 0 1 2 | 2 0 1 1 | 4 # \" 1 0 3 | 7 0 1 2 | 2 0 0 3 | 6 # \" 1 0 3 | 7 0 1 2 | 2 0 0 1 | 2 # 1 0 0 | 1 0 1 0 | 2 0 0 1 | 2 Rank(A) = 3, Rank(B) = 3. 0 1 2 | 2 1 1 1 | 5 1 0 3 | 2 1 1 1 | 5 0 1 2 | 2 1 0 3 | 2 1 1 1 | 5 0 1 2 | 2 0 1 2 | 7 1 1 1 | 5 0 1 2 | 2 0 0 0 | 9 1 0 3 | 7 0 1 2 | 2 0 0 0 | 9 1 0 3 | 7 0 1 2 | 2 0 0 0 | 1 Rank(A) = 2, Rank(B) = 3. 0 1 2 | 2 1 1 1 | 5 1 0 3 | 7 1 1 1 | 5 0 1 2 | 2 1 0 3 | 7 1 1 1 | 5 0 1 2 | 2 0 1 2 | 2 1 1 1 | 5 0 1 2 | 2 0 0 0 | 0 1 0 3 | 7 0 1 2 | 2 0 0 0 | 0 Rank( A) = 2, Rank(B) = 2.