※ 引述《pigheadthree (爬山)》之銘言：
: 題目：2*y^2 + y*e^xy + ( 4*x*y + x*e^xy + 2*y )*y'= 0
: 解法過程：設偏微分符號為m
: p = 2*y^2 + y*e^xy
: q = 4*x*y + x*e^xy + 2*y
: m(p)/my = 4*y + e^xy + x*y*e^xy
: m(q)/mx = 4*y + e^xy + x*y*e^xy + 0
: 因為 m(p)/my = m(q)/mx 所以為【正合】...............判斷！
F(x,y) = ∫ p(x,y) dx + g(y) = 2x y^2 + e^xy + g(y)
F(x,y)/my = q(x,y) = 4xy + x e^xy + g'(y) = 4xy + x e^xy + 2y
g'(y) = 2y, g(y) = y^2
F(x,y) = 2x y^2 + e^xy + y^2 = C.
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◆ From: 163.22.20.4