推 ntust661:嗚...感覺最近又要開始 ODE 了 0.0 07/07 10:02
→ mike7689:ODE是重頭戲阿~(準備重考,衝刺中)...XD 07/07 11:34
※ 引述《k0184990 (追隨夢想..)》之銘言：
: Solve the following initial value problem:
: dy/dx-2y^2+3y=1, y( 0 )=1
: ans: y=1
: 請問這題該如何解呢?
y'=2y^2-3y+1 , dy/(2y^2-3y+1) = dx , dy/[(2y-1)(y-1)] = dx
[1/(y-1) -2/(2y-1)]dy = dx
ln[y-1] - ln[2y-1] = x + c
ln[(y-1)/(2y-1)] = x + c
(y-1)/(2y-1) = C*exp^(x)
y(0)=1 , 0 = C => (y-1)/(2y-1) = 0 , y=1
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.37.175.176