Re: [理工] [工數]-ode
※ 引述《redwing119 (翼迷)》之銘言：
: 2 2 2
: (3x y +6xy+y )dx + (3x +2y)dy
: 合併好久合不出來
來賺賺P幣
M = 3x^2y + 6xy + y^2 => ρM/ρy = 3x^2 + 6x + 2y
N = 3x^2 + 2y => ρN/ρx = 6x
ρM ρN
----- - -----
ρy ρx 3x^2 + 2y
--------------- = ----------- = 1
N 3x^2 + 2y
I = exp[∫dx] = e^x
e^x[ (3x^2y + 6xy + y^2)dx + (3x^2 + 2y)dy ] = 0
=> 3x^2y(e^x)dx + 6xy(e^x)dx + y^2(e^x)dx + 3x^2(e^x)dy + 2y(e^x)dy = 0
﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋ ﹋﹋﹋﹋﹋﹋
=> d[ 3x^2y(e^x) + y^2(e^x) ] = 0
﹋﹋﹋﹋﹋﹋
=> 3x^2y(e^x) + y^2(e^x) = c
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※ 編輯: shinyhaung 來自: 112.105.70.225 (04/12 15:28)
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