Re: [理工] 積分因子&通解
※ 引述《xoo1208 (RaInBoW)》之銘言：
: Ex： 4xy+6y^2+(2x^2+6xy)y'= 0
(2xy + 3y^2)dx + (x^2 + 3xy)dy = 0
μ = x^a y^b
2(1 + b) x^(a + 1) y^b + 3(2 + b)x^a y^(b + 1)
= (2 + a)x^(a + 1) y^b + 3(a + 1)x^a y^(b + 1)
=> 2b = a
1 = a - b
=> b = 1
a = 2
=> μ = x^2 y
=> (2x^3 y^2 + 3x^2 y^3)dx + (x^4 y + 3x^3 y^2)dy = 0
Ψ = (1/2)x^4 y^2 + x^3 y^3 = C'
=> x^4 y^2 + 2 x^3 y^3 = C
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