Differentital Equations P4 Watch

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streetyfatb
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#1
Report Thread starter 14 years ago
#1
Hi,

could you please check this qu:

xdy/dx - 2y = (x^3)/(1 + x^2)

the answer i get is:

y = x^2 . arctan(x) + cx^2

Cheers

Streety
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dvs
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#2
Report 14 years ago
#2
dy/dx - (2/x)y = (x^2)/(1 + x^2)
inegrating factor = 1/x²
(1/x²)dy/dx - (2/x³)y = 1/(1 + x^2)
d(y/x²) = 1/(1 + x^2) dx
y/x² = arctan(x) + c
y = x².arctan(x) + x²c

Your answer's right.
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streetyfatb
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#3
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#3
Also if r = 2cos[2x] between Pi and minus Pi: using the forumlae for finding the area of the curve, do you get 2Pi??

Cheers

Streety
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dvs
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#4
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#4
Only if it's in polar coords.
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streetyfatb
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#5
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#5
Yep its polar co-ords, is do you get the same answer (PS cheers for checking the diff equation stuff, confident on them now.)

Streety
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dvs
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#6
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#6
Yeah, I get the same answer.
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