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From: SNC on 25 Jul 2010 01:57
Im trying to find a solution to equation DSolve[-y''[x] +
((Csc[x])^2)*y[x] == y[x]/4, y[x], x] but mathematica gives me some
strange result with expresion (-1+cos^2(x))^(1/4) in it. Why is that
and how should i interpretate this?

From: Nasser M. Abbasi on 25 Jul 2010 07:46
On 7/24/2010 10:57 PM, SNC wrote:
> Im trying to find a solution to equation DSolve[-y''[x] +
> ((Csc[x])^2)*y[x] == y[x]/4, y[x], x] but mathematica gives me some
> strange result with expresion (-1+cos^2(x))^(1/4) in it. Why is that
> and how should i interpretate this?
>

You got back y(x), which is the solution to the diff equation?

If you have initial conditions, then you can also plot y(x).

Mathematica found y(x), which satisfies the ode. I assume that you know
that a solution to an ode is a function which if substituted back into
the ode itself, it satisfies it.

I am not sure I really answered your question or not. May be it helps if
you said what you expected to see, and why the answer returned seems to
surprise you?

--Nasser


From: SNC on 26 Jul 2010 06:37
On 25 Lip, 13:46, "Nasser M. Abbasi" <n...(a)12000.org> wrote:
> On 7/24/2010 10:57 PM, SNC wrote:
>
> > Im trying to find a solution to equation DSolve[-y''[x] +
> > ((Csc[x])^2)*y[x] == y[x]/4, y[x], x] but mathematica gives me some
> > strange result with expresion (-1+cos^2(x))^(1/4) in it. Why is that
> > and how should i interpretate this?
>
> You got back y(x), which is the solution to the diff equation?
>
> If you have initial conditions, then you can also plot y(x).
>
> Mathematica found y(x), which satisfies the ode. I assume that you know
> that a solution to an ode is a function which if substituted back into
> the ode itself, it satisfies it.
>
> I am not sure I really answered your question or not. May be it helps if
> you said what you expected to see, and why the answer returned seems to
> surprise you?
>
> --Nasser

It suprised me because the solution isn't real, i'm looking for real
one, but mathematica gives me onle this.

From: J. Batista on 26 Jul 2010 06:50
I'm not sure what you are anticipating, but the result generated by
Mathematica is correct based on the information you provided. The result is
a complex mathematical expression that may look strange to you, but the y(x)
found by Mathematica satisfies the original differential equation. Don't
forget, your original differential equation hosts a transcendental
function. When we deal with transcendental functions, there is the
possibility that several solvers may end up with answers that appear to be
different, but in fact are equivalent mathematical expressions. You didn't
provide initial conditions, so I assumed a value for C[1] and C[2] (these
are the two expected constants generated by Mathematica as part of the
solution) and plotted y(x). Be careful, depending on the value of x, you
may be dealing with complex numerical values.

Regards,
J. Batista

On Sun, Jul 25, 2010 at 1:57 AM, SNC <snc(a)irc.pl> wrote:

> Im trying to find a solution to equation DSolve[-y''[x] +
> ((Csc[x])^2)*y[x] == y[x]/4, y[x], x] but mathematica gives me some
> strange result with expresion (-1+cos^2(x))^(1/4) in it. Why is that
> and how should i interpretate this?
>
>


From: Simon on 27 Jul 2010 04:17
> It suprised me because the solution isn't real, i'm looking for real
> one, but mathematica gives me onle this.

It's a linear ODE, so all solutions are a linear combination of two
basis solutions. This means that the automatically generated constants
C[1] and C[2] can be whatever you want... In particular:

FullSimplify[DSolve[-y''[x] + Csc[x]^2*y[x] == y[x]/4, y[x], x]/.{C[1]
-> a/(-1)^4^(-1), C[2] -> b/(-1)^4^(-1)},Element[x, Reals]]

yields a solution (which for real a and b) is manifestly real:

{{y[x] -> -(1/5) E^(-(1/2) Sqrt[5] ArcTanh[Cos[x]]) (-5 a + Sqrt[5] b
E^(Sqrt[5] ArcTanh[Cos[x]])) Sqrt[Abs[Sin[x]]]}}

Simon

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