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MathGroup Archive 2007

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Re: using Dsolve for equation: y'' + |y|^2y=ay

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84404] Re: using Dsolve for equation: y'' + |y|^2y=ay
  • From: daniele <danielelinaro at gmail.com>
  • Date: Fri, 21 Dec 2007 20:39:15 -0500 (EST)
  • References: <fkeo6j$2il$1@smc.vnet.net>

Hi,
I have used the command
sol = DSolve[{y''[x] + y[x] Abs[y[x]]^2 - a y[x] == 0}, y, x]
and I get a solution that uses implicit functions, i.e. the function
Solve.

Since the equation is nonlinear, I'd have a go with NDSolve instead of
DSolve. You may want to try something like

Manipulate[(
  nsol = NDSolve[{y''[x] + y[x] Abs[y[x]]^2 - a y[x] == 0, y'[0] ==
5,y[0] == 1}, y, {x, 0, 10}];
  Plot[Evaluate[y[x] /. nsol], {x, 0, 10}]
  ), {a, 0, 5}]

and replace appropriate values for the initial conditions and for the
parameter a (I don't know if the ones I've used make much sense, but
the integration works fine).

Daniele


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