E1）微分方程 Second order linear differential equation

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E1）微分方程 Second order linear differential equation
E1）微分方程
Second order linear differential equations

特征方程为4r^2-5r+1=0,r=1,1/4
所以y1=C1e^x+C2e^(x/4)
设特解y2=Asinx+Bcosx
则y2'=Acosx-Bsinx
y2''=-Asinx-Bcosx
所以-4Asinx-4Bcosx-5Acosx+5Bsinx+Asinx+Bcosx=cosx-sinx
-4B-5A+B=1,-4A+5B+A=-1
所以A=-1/17,B=-4/17
所以y=y1+y2=C1e^x+C2e^(x/4)-1/17*sinx-4/17*cosx
再问：多谢

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