推 monkps:不好意思 H大 請問有要解出Y嗎? 還是Z(T)就好? 04/09 00:32
→ honestonly:阿= = 好像是噢XDDDDDDD 04/09 00:32
※ 引述《wil0829ly (汪汪)》之銘言：
: We would like to solve the differential equation
: 2
: y'-6y=-3y
: k
: (a) Let y = z . Rewrite the equation as z'+ pz = q
: where p is independent of z.
: (b) Choose an appropriate k and solve for z(t)
: 請問這題要怎麼做呢?!
: 不知道要從哪裡下手= =
: 我照題目令 可是整理不出這樣的形式z'+ pz = q
: 謝謝!!
k dy dy dz k-1 dz
令y = z , ---- = ---- ---- = kz ----
dx dz dx dx
原ODE改寫成
k-1 k 2k
kz z' - 6z = -3z
6 -3 k+1 6 -3 k+1
z'- ---z = ---- z ,其中p = - --- ,q = ---- z
k k k k
6 -3 k+1
dz - ---zdx = ---- z dx
k k
選一個適當的k 這..我也不知道要選什麼耶..k不能等於0
k = -1
dz + 6zdx = 3dx
(D+6)z = 3
-6x 1
z = ce + ---
2
-1
又y = z
1
所以 y = --------------
-6x 1
ce + ---
2
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 118.167.138.31