Question

ODP+1)
(D²+1)x= t Cost​

Answer 1

Answer:

The characteristic polynomial is λ

3

(λ − 2)(λ − 3)2

. Thus, λ = 0 is a root

of multiplicity 3, so it contributes the basic solutions e

0x

, xe0x

, x2

e

0x

, i.e.,

1, x, x2

.

We have λ = 2 as a root of multiplicity 1, so it contributes the basic solution

e

2x

.

Finally, we have λ = 3 as a root of multiplicity 2, so it contributes the basic

solutions e

3x

, xe3x

.

The general solution of the equation is a linear combination, with arbitrary

coefficients, of the basic solutions, so the general solution is

Explanation:

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