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what does this answer by maple to dsolve mean?

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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

#778 — what does this answer by maple to dsolve mean?

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

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#779

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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#780

On 7/8/2013 7:16 AM, G. A. Edgar wrote:

>>
>> 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.
>>

(.ps typo above, meant to write solve(%,y(x)) ...

>
> 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.
>

Thanks. It might be better if Maple have added the word "solve"
there somewhere, so it is more clear that it means.

When I tried this in Mathematica, it also could not solve it
completely, but this is the answer it returned

        Solve[ ..... ==0 , y[x] ]

where .... is similar to Maple's.  The difference is that M added
the "Solve" bit. I thought this was a little bit more user-friendly
answer than just
       
           ..... = 0

regards,
--Nasser

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#781

In article <kreope$mq8$1@speranza.aioe.org>, Nasser M. Abbasi
<nma@12000.org> wrote:


> 
> Thanks. It might be better if Maple have added the word "solve"
> there somewhere, so it is more clear that it means.
> 

Consult the Maple help
?dsolve
to see what form a result of dsolve() might take.

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

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