Math Is Fun Forum

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.

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

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.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

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

The y = C part comes from

Old_Steve

Member

Registered: 2007-05-15

Posts: 17

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

Makes sense.