※ 引述《wellilin (QQ12)》之銘言：
: (x-2x^2cos2y)y'=3xsin2y-2y
: ans: x^3sin2y-x^2y
原式
(3x sin 2y - 2y)dx - (x - 2x^2 cos 2y)dy = 0
正合因子
M = 3x sin 2y - 2y , ρM/ρy = 6x cos 2y - 2
N = -x + 2x^2 cos 2y , ρN/ρx = -1 + 4x cos 2y
ρM ρN
---- - ----
ρy ρx 2x cos 2y - 1 1
------------- = ----------------- = ---
N 2x^2 cos 2y - x x
1
I = exp [∫--- dx] = x
x
同乘 x 可得
2 2 3
3x sin 2y dx - 2xy dx - x dy + 2x cos 2y dy = 0
3 2
d(x sin2y) - d(x y) = 0
x^3sin2y - x^2y = 0
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