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工程數學 微分問題
小弟才剛入門工數，很求一些題目作法解析https://i.imgur.com/X53ae2o.jpg
<div></div> I will try to do (4) for you:
x dy/dx + y = 0
x dy/dx = -y
-1/y dy = 1/x dx
Integrate both sides, log(x) = -log(y) + C
log(x) = -log(y) + log(k)
log(x) = log(k/y)
x = k/y where k is a constant
y(4) = 6, so k = 24
The answer is x = 24/y or y = 24/x or xy = 24
QED
Similarly, (2) can be solved:
y dy/dx + 36x =0
y dy = -36x dx
so, y^2 +36x^2 = C
y = (-36x^2 +C)^0.5
QED avontube 發表於 2021-7-24 11:05 PM static/image/common/back.gif
I will try to do (4) for you:
x dy/dx + y = 0
thanks Your help is much appreciated {:2:}
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