Re: [微積] 一題很簡單的微分方程式
※ 引述《dkcheng (電磁霸主)》之銘言：
: Solve x^2(y+1)dx+y^2(x-1)dy=0
分離變數法
x^2 -y^2
------------ dx = ---------------- dy
x-1 y+1
x^2/(x-1)
假分式 可用長除法 x +1
x-1 ∕￣￣￣￣￣￣￣￣￣
x^2
x^2 -x
-------------------------
x
x +1
---------------------
-1
x^2 -x +x-1 +1 1
-------------------- = x +1 + -----------
x-1 x-1
同理y部份就不做
x^2/2 + x+ ln (x-1) = -y^2/2 +y- ln(y+1) +c
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