Re: [微積] 請教兩題積分
: 上面的答案是我寫錯的
1.
y' + 3x^12 y = x^13
Iy' + 3Ix^12 y = Ix^13
設I' = 3Ix^12 => (lnI)' = 3x^12
I = exp((1/13)x^13)
[Iy]' = Ix^13
y = (1/I)∫Ix^13 dx
2.
cosx y' - sinx y = sin(138x)
(cosx y)' = sin(138x)
cosx y = -(1/138)cos(138x) + C
y = -(1/138)[cos(138x) + C]/cos(x)
= -(1/138)cos(138x)/cos(x) + c'/cos(x)
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