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#1 2007-05-26 01:04:07

Old_Steve
Member
Registered: 2007-05-15
Posts: 17

Can't get it - Diff Eq. Problem

y" + y*(y')^3 = 0

Let v = y' therfore v'= f(y.v) which uses variables x, y & z  eliminate x by thinking of y as independent  via chain rule v*(dv/dy) = f(y.v)  There will be two constants in the final result

I having trouble setting up and solving.

Thanks for any help.

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#2 2007-05-26 01:46:39

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Can't get it - Diff Eq. Problem

So the original differential equation becomes

If v = 0, then y is a constant function. Otherwise

Hence the solution is

or

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#3 2007-05-26 05:28:50

Old_Steve
Member
Registered: 2007-05-15
Posts: 17

Re: Can't get it - Diff Eq. Problem

I hate to be ignorant but I don't really follow the first line.  And, I missed how y=C. 

Can you point me in the right direction.  I need to get this down or I will never make it.

Thanks.

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#4 2007-05-26 07:43:21

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Can't get it - Diff Eq. Problem

The y = C part comes from

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#5 2007-05-26 07:55:47

Old_Steve
Member
Registered: 2007-05-15
Posts: 17

Re: Can't get it - Diff Eq. Problem

Makes sense.

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