“Variation of Parameters”的概念、定义、习题解题方法及翻译-数学辞典

单词

Variation of Parameters

释义

Variation of Parameters

For a second-order Ordinary Differential Equation,

(1)

Assume that linearly independent solutions

and

are known. Find

and

such that

			(2)
			(3)

Now, impose the additional condition that

(4)

so that

			(5)
			(6)

Plug

, and

back into the original equation to obtain

(7)

(8)

Therefore,

			(9)
			(10)

Generalizing to an th degree ODE, let , ..., be the solutions to the homogeneous ODE and let ,..., be chosen such that

(11)

Then the particular solution is

(12)

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