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求微分方程的通解.

问答题
2021-07-18 12:48
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正确答案
解:1)求对应的齐次方程的通解:

    由特征方程得特征根为,故通解为
2)求原方程的一个特解:

依题意设原方程的一个特解形式为
代入原方程中得到

所以,原方程的通解为

试题解析
解:1)求对应的齐次方程的通解:

    由特征方程得特征根为,故通解为
2)求原方程的一个特解:

依题意设原方程的一个特解形式为
代入原方程中得到

所以,原方程的通解为

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