If 2e 4x - 6e x is in the solution set for a linear, 2nd order, constant coeffic

Question

If 2e4x - 6ex is in the solution set for a linear, 2nd order, constant coefficient, homogeneous ODE, then an a If 2e4x - 6ex is in the solution set for a linear, 2nd order, constant coefficient, homogeneous ODE, then an appropriate form for the associated characteristic equation would be Question 4 options: A) a2 = 0 B) a2 -2a = 0 C) a2 + 3a = 0 D) a2 - 2a + 1 = 0 E) a2 + 4a + 4 = 0 F) a2 - 5a + 6 = 0 G) a2 - a - 6 = 0 H) a2 + a - 6 = 0 I) a2 + 5a + 6 = 0 J) none of these If 2e4x - 6ex is in the solution set for a linear, 2nd order, constant coefficient, homogeneous ODE, then an a If 2e4x - 6ex is in the solution set for a linear, 2nd order, constant coefficient, homogeneous ODE, then an appropriate form for the associated characteristic equation would be If 2e4x - 6ex is in the solution set for a linear, 2nd order, constant coefficient, homogeneous ODE, then an a A) a2 = 0 B) a2 -2a = 0 C) a2 + 3a = 0 D) a2 - 2a + 1 = 0 E) a2 + 4a + 4 = 0 F) a2 - 5a + 6 = 0 G) a2 - a - 6 = 0 H) a2 + a - 6 = 0 I) a2 + 5a + 6 = 0 J) none of these A) a2 = 0 B) a2 -2a = 0 C) a2 + 3a = 0 D) a2 - 2a + 1 = 0 E) a2 + 4a + 4 = 0 F) a2 - 5a + 6 = 0 G) a2 - a - 6 = 0 H) a2 + a - 6 = 0 I) a2 + 5a + 6 = 0 J) none of these A) a2 = 0 B) a2 -2a = 0 C) a2 + 3a = 0 D) a2 - 2a + 1 = 0 E) a2 + 4a + 4 = 0 F) a2 - 5a + 6 = 0 G) a2 - a - 6 = 0 H) a2 + a - 6 = 0 I) a2 + 5a + 6 = 0 J) none of these

Explanation / Answer

G.

a2 - a - 6 = 0

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