y''-y=xsinx y(0)=y'(0)=0y''-y=xsinx y(0)=y'(0)=0
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y''-y=xsinx y(0)=y'(0)=0y''-y=xsinx y(0)=y'(0)=0
y''-y=xsinx y(0)=y'(0)=0
y''-y=xsinx y(0)=y'(0)=0
y''-y=xsinx y(0)=y'(0)=0y''-y=xsinx y(0)=y'(0)=0
特征方程为r^2-1=0,得r=1,-1
设特解y*=(ax+b)sinx+(cx+d)cosx
则y*'=asinx+(ax+b)cosx+ccosx-(cx+d)sinx=(a-cx-d)sinx+(ax+b+c)cosx
y*"=-csinx+(a-cx-d)cosx+acosx-(ax+b+c)sinx=-(ax+b+2c)sinx+(-cx-d+2a)cosx
代入方程:-(ax+b+2c+ax+b)sinx+(-cx-d+2a-cx-d)cosx=xsinx
对比系数得:-2a=1,2b+2c=0,-2c=0,2a-2d=0
解得:a=-0.5,b=c=0,d=-0.5
所以通解为y=C1e^x+C2e^(-x)-0.5xsinx-0.5cosx
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