Re: [理工] [工數]-一階ODE2
※ 引述《kusorz (^~^)》之銘言：
: 我寫到變成d(x+y)就寫不下去了
: y'+(x+y)x=x^3(x+y)^3-1
: ans: 1 x^2
: _______ = (1+x^2)+ce
: (x+y)^2
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y'+ (x+y)x = x^3(x+y)^3 - 1
→ d(x+y) + (x+y)x dx = x^3(x+y)^3 dx
→ d(x+y)^2 + 2x(x+y)^2 dx = 2x^3(x+y)^4 dx
→ d[1/(x+y)^2] - 2x/(x+y)^2 dx = -2x^3 dx
→ d[1/(x+y)^2] + 1/(x+y)^2 d(-x^2) = x^2 d(-x^2)
→ d[e^(-x^2) / (x+y)^2] = d[(1+x^2)*e^(-x^2)]
→ e^(-x^2) / (x+y)^2 = (1+x^2)*e^(-x^2) + c
or 1/(x+y)^2 = (1+x^2) + c*e^(x^2)
其實依序假設 x+y = t 、 m = t^2 、 n = 1/m
就能觀察到 O.D.E. 如何變成 linear
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◆ From: 220.132.28.221
※ 編輯: doom8199 來自: 220.132.28.221 (07/20 02:34)
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