推 wil0829ly:沒錯 是這答案 非常謝謝你!! 04/08 21:57
※ 引述《wil0829ly (汪汪)》之銘言：
: Consider the differential equation
: dy 2
: x──-4x y +2ylny = 0
: dx
: Find an integrating factor ρ(x, y)
: so that the multiplication of the differential
: equation by ρ(x, y) yields an exact differential equation.
: 這題我是先把ρ(x, y)乘到ODE 所以ODE變exact
: 在用判別式讓他相等 可是我還是解不出來= =
2 1
xdy - 4x ydx + 2ylnydx = 0 //同乘----
xy
1 lny
---dy - 4xdx + 2 -----dx = 0
y x
2
d(lny) + ---lnydx = 4xdx //一階線性
x
2 2
I = exp[∫---dx] = x
x
x
ρ(x, y) = ---??
y
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