Find A and B in y=Asinx+Bcosx so that y''-y=sinx.达人应该知道y''是y的导数的导数!

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Find A and B in y=Asinx+Bcosx so that y''-y=sinx.达人应该知道y''是y的导数的导数!

Find A and B in y=Asinx+Bcosx so that y''-y=sinx.达人应该知道y''是y的导数的导数!
Find A and B in y=Asinx+Bcosx so that y''-y=sinx.
达人应该知道y''是y的导数的导数!

Find A and B in y=Asinx+Bcosx so that y''-y=sinx.达人应该知道y''是y的导数的导数!
y'=Acosx-Bsinx
y''=-Asinx-Bcosx
因为y''-y=sinx.
所以-Asinx-Bcosx-(Acosx-Bsinx)=sinx
sinx(1+A-B)+cosx(B+A)=0
所以1+A-B=0
A+B=0
解得A=-1/2
B=1/2

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