Has this old saw ever been answered?

Does the differential equation:

dy/dx=1/x+1/y

have a solution in terms of elementary functions?

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- Jul 14th 2006, 02:52 PM #1

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- Jul 15th 2006, 10:23 AM #2

- Jul 15th 2006, 01:38 PM #3

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- Jul 15th 2006, 04:19 PM #4

- Jul 15th 2006, 04:25 PM #5

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- Jul 15th 2006, 06:19 PM #6

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I did try to solve this but alas I am having little success.

Rewrite,

Note, this is a*non-homogenous*.

Thus, begin by finding the general solution of,

Thus,

Note, this is a*Bernoulli, equation*

Use substitution,

Thus,

.

Thus,

Thus,

Thus,

Thus,

---> general solution.

For the particiluar solution for this ode I had trouble. I went threw many different attempt non of them work. So maybe this is no elementary function which satisfies this particular condition.

- Jul 16th 2006, 05:22 AM #7

- Jul 16th 2006, 06:12 AM #8

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- Jul 16th 2006, 06:41 AM #9

- Jul 16th 2006, 08:03 AM #10

- Jul 16th 2006, 08:21 AM #11

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