Find an auxiliary equation for the ODE y\'\' + 2y\' - 8y = 0 . Question 3 option

Question

Find an auxiliary equation for the ODE y'' + 2y' - 8y = 0 . Question 3 options: A) (a - 1)(a + 2) = 0 B) (a - 1)(a + 3) = 0 C) (a - 1)(a + 4) = 0 D) (a - 1)(a + 5) = 0 E) (a - 2)(a + 1) = 0 F) (a - 2)(a + 3) = 0 G) (a - 2)(a + 4) = 0 H) (a - 3)(a + 1) = 0 I) (a - 3)(a + 2) = 0 J) (a - 3)(a + 4) = 0 K) none of these
Please show your work!! Find an auxiliary equation for the ODE y'' + 2y' - 8y = 0 . Find an auxiliary equation for the ODE y'' + 2y' - 8y = 0 . A) (a - 1)(a + 2) = 0 B) (a - 1)(a + 3) = 0 C) (a - 1)(a + 4) = 0 D) (a - 1)(a + 5) = 0 E) (a - 2)(a + 1) = 0 F) (a - 2)(a + 3) = 0 G) (a - 2)(a + 4) = 0 H) (a - 3)(a + 1) = 0 I) (a - 3)(a + 2) = 0 J) (a - 3)(a + 4) = 0 K) none of these
A) (a - 1)(a + 2) = 0 B) (a - 1)(a + 3) = 0 C) (a - 1)(a + 4) = 0 D) (a - 1)(a + 5) = 0 E) (a - 2)(a + 1) = 0 F) (a - 2)(a + 3) = 0 G) (a - 2)(a + 4) = 0 H) (a - 3)(a + 1) = 0 I) (a - 3)(a + 2) = 0 J) (a - 3)(a + 4) = 0 K) none of these Please show your work!! A) (a - 1)(a + 2) = 0 B) (a - 1)(a + 3) = 0 C) (a - 1)(a + 4) = 0 D) (a - 1)(a + 5) = 0 E) (a - 2)(a + 1) = 0 F) (a - 2)(a + 3) = 0 G) (a - 2)(a + 4) = 0 H) (a - 3)(a + 1) = 0 I) (a - 3)(a + 2) = 0 J) (a - 3)(a + 4) = 0 K) none of these

Explanation / Answer

from the equation:

a^2 + 2a - 8 = 0

(a+4)(a-2) = 0

answer G.

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