推 topee:感謝你^^ 真的很感謝~~ 03/23 17:57
※ 引述《topee (eason)》之銘言：
: ※ 引述《topee (eason)》之銘言：
: : 2
: : v = ----x^3 + c
: : 9
: : 2
: : y^2/3 = --- x^5 + cx^2
: : 9
: : 2 7
: : 1 = --- + c c= ---
: : 9 9
: 已修正.......請問一下 還有錯嗎..我微分回去也怪怪的
我算算看囉~
3
y'- ---y = x^4 y^1/3 y(1)=1
x
令u = y^[1-(1/3)] = y^(2/3)
du dy 3
── = (2/3) y^(-1/3)*── = (2/3) y^(-1/3)*[x^4 y^(1/3) + ──y]
dx dx x
du 2
── = (2/3)x^4 + ── y^(2/3)
dx x
du 2
── - ──u = (2/3)x^4...(1) (u = y^(2/3)代入)
dx x
2
∫(-─)dx
x -2 ln│x│ 1
I.F.= e = e = ──
x^2
1
(1)乘以── 得
x^2
1 du 2
── ── - ── u = (2/3)x^2
x^2 dx x^3
d 1
─ [── u] = (2/3)x^2
dx x^2
1
── u = ∫(2/3)x^2 dx = (2/9)x^3 + c
x^2
u = y^(2/3)代入得
y^(2/3)
─── = (2/9)x^3 + c
x^2
y(1)=1代入得
1
── = 2/9 + c
1
c= 7/9
所以您的答案是對的~
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