推 h042910276 : 原來如此~謝謝 02/26 15:07
※ 引述《h042910276 (原罪修羅)》之銘言：
: 第一題
: http://i.imgur.com/MAPnJvz.jpg
: 請問一下最後將兩式合成原函數
: 為什麼不是x+y+2(x^2+y^2)/(x+y)
ψ(x, y)
= x + 2(y^2)/[x + y] + f(y)
= y + 2(x^2)/[x + y] + g(x)
= [x^2 + xy + 2y^2 + xf(y) + yf(y)]/[x + y]
= [2x^2 + xy + y^2 + xg(x) + yg(x)]/[x + y]
g(x) = -x + c
f(y) = -y + c
=> ψ(x , y) = [x^2 + y^2]/[x + y] = c
: 第二題
: 綠色框中要怎麼使用合併法合成下面的
: d(-y/xcosx)
[@/@x]{-1/[xcos(x)]}
= [cos(x) - xsin(x)]/[xcos(x)]^2
= [1 - xtan(x)]/[cos(x) x^2]
= [@/@y]{y[1 - xtan(x)]/[cos(x) x^2]}
=> [@/@x]{-y/[xcos(x)] + f(x)} = y[1 - xtan(x)]/[cos(x) x^2] + f'(x)
=> f(x) = c
所以
y[1 - xtan(x)]/[cos(x) x^2] dx + {-1/[xcos(x)]} dy
= d[-y/[xcos(x)]]
: http://i.imgur.com/rBsUgh9.jpg
: 謝謝
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