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Annihilator Method answer not the same as in Maple 15

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  Annihilator Method answer not the same as in Maple 15 anon <anon@anon.com> - 2011-12-26 01:05 +0000
    Re: Annihilator Method answer not the same as in Maple 15 Axel Vogt <&noreply@axelvogt.de> - 2011-12-26 08:49 +0100
      Re: Annihilator Method answer not the same as in Maple 15 anon <anon@anon.com> - 2011-12-26 15:39 +0000
    Re: Annihilator Method answer not the same as in Maple 15 "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2011-12-26 07:41 -0700
      Re: Annihilator Method answer not the same as in Maple 15 anon <anon@anon.com> - 2011-12-26 15:37 +0000

#270 — Annihilator Method answer not the same as in Maple 15

I plugged in:

ode:=diff(y(t),t,t)+y(t)=cos(t);
dsolve(ode);

and the answer Maple 15 displayed was:

y(t)=sin(t)_C2+cos(t)_C1+(1/2)*cos(t)+(1/2)*t*sin(t)

I know this is the solution but when I use the Annihilator Method on 
paper, I get the same answer but without the (1/2)*cos(t)

y(t) = c1*sin(t) + c2*cos(t) + (1/2)*t*sin(t)

This answer also checks out but my question is:  What method does 
Maple 15 use to get the (1/2)*cos(t) term?

Thank you.


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#271

On 26.12.2011 02:05, anon wrote:
> I plugged in:
>
> ode:=diff(y(t),t,t)+y(t)=cos(t);
> dsolve(ode);
>
> and the answer Maple 15 displayed was:
>
> y(t)=sin(t)_C2+cos(t)_C1+(1/2)*cos(t)+(1/2)*t*sin(t)
>
> I know this is the solution but when I use the Annihilator Method on
> paper, I get the same answer but without the (1/2)*cos(t)
>
> y(t) = c1*sin(t) + c2*cos(t) + (1/2)*t*sin(t)
>
> This answer also checks out but my question is:  What method does
> Maple 15 use to get the (1/2)*cos(t) term?
>
> Thank you.

After simplification it is just a different naming for the constants:

   sin(t)*_C2+cos(t)*_C1+(1/2)*cos(t)+(1/2)*t*sin(t);
   simplify(%, size);

     1/2*(2*_C1+1)*cos(t)+1/2*sin(t)*(2*_C2+t)


   c1*sin(t) + c2*cos(t) + (1/2)*t*sin(t);
   simplify(%, size);

     1/2*(2*c1+t)*sin(t)+c2*cos(t)

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#274

Thank you.  I found that term appears when using variation of 
paramters method.


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#272

In article <DLPJq.1901$ae4.1295@newsfe01.iad>, anon <anon@anon.com>
wrote:

> I plugged in:
> 
> ode:=diff(y(t),t,t)+y(t)=cos(t);
> dsolve(ode);
> 
> and the answer Maple 15 displayed was:
> 
> y(t)=sin(t)_C2+cos(t)_C1+(1/2)*cos(t)+(1/2)*t*sin(t)
> 
> I know this is the solution but when I use the Annihilator Method on 
> paper, I get the same answer but without the (1/2)*cos(t)
> 
> y(t) = c1*sin(t) + c2*cos(t) + (1/2)*t*sin(t)
> 
> This answer also checks out but my question is:  What method does 
> Maple 15 use to get the (1/2)*cos(t) term?
> 
> Thank you.

What do you get if you use variation of parameters?

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

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#273

LoL!  The (1/2)*cos(t) term popped up using variation of parameters 
method.  Thank you and Merry Christmas, if you celebrate it, if not 
then I take it back.  :D

In article <DLPJq.1901$ae4.1295@newsfe01.iad>, anon <anon@anon.com>
wrote:

> I plugged in:
> 
> ode:=diff(y(t),t,t)+y(t)=cos(t);
> dsolve(ode);
> 
> and the answer Maple 15 displayed was:
> 
> y(t)=sin(t)_C2+cos(t)_C1+(1/2)*cos(t)+(1/2)*t*sin(t)
> 
> I know this is the solution but when I use the Annihilator Method 
on 
> paper, I get the same answer but without the (1/2)*cos(t)
> 
> y(t) = c1*sin(t) + c2*cos(t) + (1/2)*t*sin(t)
> 
> This answer also checks out but my question is:  What method does 
> Maple 15 use to get the (1/2)*cos(t) term?
> 
> Thank you.

What do you get if you use variation of parameters?

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


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