推 WuLow:感謝高手版大! 02/28 19:39
推 jay31820:北科題目 我也解好久 感謝高手中高手版大 02/28 23:52
※ 引述《WuLow (5F)》之銘言：
: y'=(ylny/x) y(1/e)=e
Variable of Seperation
dy dx
─── = ──
y lny x
lnlny = lnx + c1
lny = c1 x
c1 x
y = e , I.C. y(1/e) = e
c1 (1/e) 1
e = e = e , c1 = e
ex
Particular solution y = e
: x^2y''=(y')^2+2xy'
2 2
x y'' - 2xy' = (y')
4 y' 2
x ( ── )' = (y')
x^2
(y')
─── = u
x^2
2 du 1
u' = u , ─── = dx , - ── = x + c1
u^2 u
-1 y'
──── = ───
x + c1 x^2
2
-x
y' = ────
x + c1
2 2 2
x - c1 + c1
dy = - ─────── dx
x + c1
2
c1
dy = - [ x + c1 + ──── ] dx
x + c1
2
x 2
y = - ── - c1 x - c1 ln│ x + c1│ + c2
2
: 請問高手這幾題怎麼算
: 謝謝指教!!!
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