Find the general solution of the given higher-order differential equation. y''' + 3y'' + 3y' + y = 0

Step-by-step explanation:

We can determine the characteristic equation all we have to do is:

let y' = m, hence y" = m², y'" = m³

Therefore, the higher-order differential equation becomes:

m³ + 3m² + 3m + 1 = 0

(m + 1)(m² + 2m + 1) = 0

(m + 1)(m + 1)(m + 1) = 0

(m + 1)³ = 0

m = -1, -1, -1

Therefore the general solution is given as:

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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