Re: [理工] [工數]-一階ODE
※ 引述《JaLunPa (呷懶趴)》之銘言：
: 6xy+2y+8+xy'=0
6x+2
=> y' + ______ y = -8/x
x
=> I=x^2*e^(6x) , yI = ∫I*-8/x dx + c
=> y=cx^(-2)*e^(-6x) - 4/3x + 2/9x^(-2)
: 答案是y=cx^-2 * e^-6x - 4/3x + 2/9x^2
: (x-y^2)dx+y(1+x)dy=0
y x
=> y'= ______ - ______
x+1 y(x+1)
let t = y^2 , t' = 2yy'
=> 1 1 x
___ t' = ____ t - _____
2 x+1 x+1
2 -2x
=> t' - _______ t = _____
(1+x) x+1
線性 跟上一題一樣
有錯誤請多指教
: 答案y^2-2x-1=c(x+1)^2
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