→ boy210637:這題根本就是在考積化和差= = 01/21 21:41
推 msu:感謝您^^ 01/21 21:44
※ 引述《iyenn (曉風)》之銘言：
: ※ 引述《msu (do my best)》之銘言：
: : 1.cosydx+(1+e^(-x))sinydy=0, y(0)=pi/4
: cosy=u sinyy'=-u'
: - du dx
: ----+------=0
: u 1+e^-x
: -lnu - lne^-x +ln(1+e^-x)=c'
: (1+e^x)/cosy=c
: y(0)=pi/4
: c=2*2^1/2
: : 2. cos2x
: : y'=----------------------------
: : cos(x+y) + sin(x-y)
[cos(x)]^2 - [sin(x)]^2
dy = ---------------------------------------------------
cos(x)cos(y)-sin(x)sin(y)+sin(x)cos(y)-cos(x)sin(y)
交叉相乘
cos(x)d[sin(y)] + sin(x)d[cos(y)] + sin(x)d[sin(y)] + cos(x)d[cos(y)]
= { [cos(x)]^2 -[sin(x)]^2 }dx
[sin(x) + cos(x)]{ d[(siny)] + d[cos(y)] } = { [cos(x)]^2 -[sin(x)]^2 }dx
d[sin(y)] + d[cos(y)] = [ cos(x) - sin(x) ]dx
sin(y) + cos(y) = sin(x) + cos(x) + C
: : 請問這幾題如何解呢?
: : 感謝^^
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※ 編輯: boy210637 來自: 220.136.65.65 (01/21 21:26)