E1)微分方程 Second order linear differential equationE1)微分方程Second order linear differential equations

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E1)微分方程 Second order linear differential equationE1)微分方程Second order linear differential equations
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E1)微分方程 Second order linear differential equationE1)微分方程Second order linear differential equations
E1)微分方程 Second order linear differential equation
E1)微分方程
Second order linear differential equations

E1)微分方程 Second order linear differential equationE1)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