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Re: what does this answer by maple to dsolve mean?

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In article <krddud$3gs$1@speranza.aioe.org>, Nasser M. Abbasi
<nma@12000.org> wrote:

> Maple 17.01 on windows.
> 
> -------------------------
> restart;
> ode146:=x^2*diff(y(x),x)+a*y(x)^2+x*y(x)^3=0:
> dsolve(%,y(x));
> -------------------------
> 
> answer is
> 
> 
> _C1+(x+(1/2)*a*sqrt(Pi)*sqrt(2)*erf((1/2)*sqrt(2)*
> (a*y(x)+x)/(y(x)*x))*exp((1/2)*(a*y(x)+x)^2/(y(x)^2*x^2)))*
> exp(-(1/2)*((a-x)*y(x)+x)*((a+x)*y(x)+x)/(y(x)^2*x^2)) = 0
> 
> I was expecting an answer such as y(x)= ... some function of x
> 
> But the above is just ... some function of x = 0
> 
> what happend to the y(x)=... format in this case?
> 
> Did this happen becuase it can't find a solution for
> y(x) from the final answer it gave at the end? since
> doing solve(%,x) did not evaluate.
> 
> thanks,
> --Nasser


This is known as an "implicit" solution.  If one could solve that
equation for y(x), that would be the answer you want.  But of course
there is no closed-form solution, which is why Maple writes only the
implicit form.

-- 
G. A. Edgar                              http://www.math.ohio-state.edu/~edgar/

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what does this answer by maple to dsolve mean? "Nasser M. Abbasi" <nma@12000.org> - 2013-07-07 23:07 -0500
  Re: what does this answer by maple to dsolve mean? "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2013-07-08 06:16 -0600
    Re: what does this answer by maple to dsolve mean? "Nasser M. Abbasi" <nma@12000.org> - 2013-07-08 11:18 -0500
      Re: what does this answer by maple to dsolve mean? "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2013-07-09 05:20 -0600

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