Variation of parameters: the first determining condition and its effect on yp' (Q1664)

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Variation of parameters: the first determining condition and its effect on yp'
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    Statements

    y_{p}=u_{1}y_{1}+u_{2}y_{2}\\quad\\Rightarrow\\quad y_{p}'=u_{1}'y_{1}+u_{2}'y_{2}+u_{1}y_{1}'+u_{2}y_{2}';\\qquad u_{1}'y_{1}+u_{2}'y_{2}=0\\ \\Rightarrow\\ y_{p}'=u_{1}y_{1}'+u_{2}y_{2}'
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