Re: [理工] [工數]-一階ODE
※ 引述《mdpming (★pigming★)》之銘言:
: 1.
: 3 2 3 2
: (- ---x cos2y)dx+(xsin2y + y )dy = 0
: 2
: 答案是
: 1 3 1 3
: ---y = x+ ---xcos2y
: 3 2
: 算到這邊 要賣向高階ode啦~
3 2 3 2
(- ---x cos2y)dx+(xsin2y + y )dy = 0
2
3x^2sin2y=3x^2sin2y
正合,直接偏積分
-1
Φ(x,y)=(---x^3)cos2y+f(y)
2
-1 1
Φ(x,y)=(---x^3)cos2y+---y^3+f(x)
2 3
-1 1
Φ(x,y)=(---x^3)cos2y+---y^3=c
2 3
x貌似是常數c打錯了?
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◆ From: 123.193.214.165
※ 編輯: iyenn 來自: 123.193.214.165 (08/05 22:58)
※ 編輯: iyenn 來自: 123.193.214.165 (08/05 22:59)
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08/05 23:02, , 1F
08/05 23:02, 1F
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08/06 01:34, 17F
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