望采纳谢谢啦
y''-y= (sinx)^2
y''-y = (1/2)(1- cos2x)
let
yp = Acos2x +Bsin2x +C
yp'=-2Asin2x+2Bcos2x
yp''=-4Acos2x-4Bsin2x
yp''-yp = (1/2)(1- cos2x)
-5Acos2x -5Bsin2x - C = (1/2)(1- cos2x)
A= 2/5, B=0, C= -1/2
yp = (2/5)cos2x - 1/2
The aux. equation
p^2 - 1 =0
p= 1 or -1
let
yg = De^x +Ee^(-x)
y''-y= (sinx)^2
y= yg+yp =De^x +Ee^(-x) + (2/5)cos2x - 1/2
[高数]变限积分求导易错点
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