On 7 nov, 09:57, Patrick Coilland <pcoill...@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)?
> On 7 nov, 09:57, Patrick Coilland <pcoill...@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
obviously not, since it exists solutions neither odd, neither even.
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) ...
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