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| daniel D... |
 Posted: Fri Nov 06, 2009 6:19 pm |
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Hi,
I came across the following differential equation:
sqrt(1+(y')^2)=(d/dx)((yy')/sqrt(1+(y')^2))
I found a possible solutions: y(x)=cosh(x+C1).
However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees.
Can anyone find it?
Thank you. |
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| alainverghote at (no spam) gmail.com... |
| Posted: Sat Nov 07, 2009 3:00 am |
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On 7 nov, 09:57, Patrick Coilland <pcoill... at (no spam) pcc.fr> wrote:
[quote]daniel D a écrit :
Hi,
I came across the following differential equation:
sqrt(1+(y')^2)=(d/dx)((yy')/sqrt(1+(y')^2))
I found a possible solutions: y(x)=cosh(x+C1).
However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees.
Can anyone find it?
(cosh(ax+b))/a
[/quote]
Dear Friends,
Without solving it
does it exist a way to give the parity of the solutions y(x)?
Alain |
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| daniel D... |
| Posted: Sat Nov 07, 2009 3:16 am |
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| Patrick Coilland... |
| Posted: Sat Nov 07, 2009 3:57 am |
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daniel D a écrit :
[quote]Hi,
I came across the following differential equation:
sqrt(1+(y')^2)=(d/dx)((yy')/sqrt(1+(y')^2))
I found a possible solutions: y(x)=cosh(x+C1).
However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees.
Can anyone find it?
[/quote]
(cosh(ax+b))/a |
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| Patrick Coilland... |
| Posted: Sat Nov 07, 2009 9:09 am |
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alainverghote at (no spam) gmail.com a écrit :
[quote]On 7 nov, 09:57, Patrick Coilland <pcoill... at (no spam) pcc.fr> wrote:
daniel D a écrit :
Hi,
I came across the following differential equation:
sqrt(1+(y')^2)=(d/dx)((yy')/sqrt(1+(y')^2))
I found a possible solutions: y(x)=cosh(x+C1).
However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees.
Can anyone find it?
(cosh(ax+b))/a
Dear Friends,
Without solving it
does it exist a way to give the parity of the solutions y(x)?
Alain
[/quote]
obviously not, since it exists solutions neither odd, neither even. |
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| alainverghote at (no spam) gmail.com... |
| Posted: Sat Nov 07, 2009 11:16 pm |
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Guest
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On 7 nov, 14:16, daniel D <x1... at (no spam) x.com> wrote:
[quote]Thank you very much.
[/quote]
Good morning,
Never an explanation was given about the proposed solutions...
May be some tracks were interesting:
1) non-contradiction inside LHS and RHS for an even function y(x),
2) stability of the equation for the transformation
y(x)=> y(ax+b)/a ,
3)a whiff of trig in sqrt(1+(y')^2) ...
Well,I am not a 'matlab or maple-totaller'
Alain |
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