工程數學 微分問題

u937121672

小弟才剛入門工數，很求一些題目作法解析

avontube

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

avontube

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

u937121672

avontube 發表於 2021-7-24 11:05 PM

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I will try to do (4) for you:

x dy/dx + y = 0

thanks   Your help is much appreciated ...

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