Линейное неоднородное уравнение второго порядка с постоянными коэффициентами y''...

July 2022 1 32 Report

Линейное неоднородное уравнение второго порядка с постоянными коэффициентами y''-y=2e^x

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$y''-y=2e^x\\\lambda^2-1=0\\\lambda_{1,2}=^+_-1\\Y=C_1e^x+C_2e^{-x}\\\hat{y}=Axe^x\\\hat{y}'=Ae^x+Axe^x\\\hat{y}''=2Ae^x+Axe^x\\\\2Ae^x+Axe^x-Axe^x=2e^x\\2Ae^x=2e^x\\A=1\\\hat{y}=xe^{x}\\y=Y+\hat{y}=C_1e^x+C_2e^{-x}+xe^{x}$

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