[sage-support] Re: Laplace solve:
You sir...
Are...
a genius.
On Nov 11, 12:13 pm, David Joyner wrote:
> On Wed, Nov 11, 2009 at 3:10 PM, Jaasiel Ornelas wrote:
>
> > I'm using:
>
> > Sage Version 4.1.1, Release Date: 2009-08-14
>
> Okay. The above was done with Sage 4.2, so may or may not work in your
> version.
>
>
>
> > We just started laplace in my class, so I did not know that laplace
> > transforms don't solve non linear ode's. Sorry :p
>
> > On Nov 11, 12:01 pm, David Joyner wrote:
> >> On Wed, Nov 11, 2009 at 1:19 PM, Jaasiel Ornelas
> >> wrote:
>
> >> > I can't get desolve_laplace to give me a good output. I had already
> >> > tried the regular solve (desolve) and it gave to told me that it
> >> > cannot solve that equation. This is my code:
>
> >> > sage: (g,t) = var('g,t')
>
> >> > sage: y=function('y',t)
>
> >> > sage: DEiii = pi * (39/100*y + 1/2)^2* diff(y,t) + a * sqrt(2*g*y)
>
> >> This is a non-linear ODE. You can't use Laplace transforms
> >> to solve such ODEs.
>
> >> However, it is separable and I can solve a slightly simpler version:
>
> >> sage: t = var("t")
> >> sage: y = function("y",t)
> >> sage: DE = y^2*diff(y,t)+sqrt(y)==0
> >> sage: desolve(DE,[y,t])
> >> -2/5*y(t)^(5/2) == c + t
>
> >> Which version of Sage are you using?
>
> >> > sage: a = .5^2*pi
>
> >> > sage: DEiii
>
> >> > 1/1*(39*y(t) + 50)^2*pi*D[0](y)(t) + 0.250*pi*sqrt(g*y
> >> > (t))*sqrt(2)
>
> >> > sage: desolve(DEiii, [y,t])
> >> > Traceback (most recent call last):
> >> > ...
> >> > NotImplementedError: Maxima was unable to solve this system.
>
> >> > sage: desolve_laplace(DEiii, ["t","y"], [0,50,0])
> >> > "?%ilt(-(1521*'laplace('y(t)^2*'diff('y(t),t,1),t,false)+3900*'laplace
> >> > ('y(t)*'diff('y(t),t,1),t,false)+2500*sqrt(2)*'laplace(sqrt(g*'y
> >> > (t)),t,false)-125000)/(2500*false),false,t)"
>
> >> > Perhaps it's because I can't understand the output, but if anyone
> >> > could help me with this, thank you.
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[sage-support] Re: Laplace solve:
On 11 lis, 21:10, Jaasiel Ornelas wrote: > I'm using: > > Sage Version 4.1.1, Release Date: 2009-08-14 > > We just started laplace in my class, so I did not know that laplace > transforms don't solve non linear ode's. Sorry :p > Are you student? If you put your equation (with a written as (1/2) ^2*pi and g=1) pi * (39/100*y + 1/2)^2* y' + (1/2)^2*pi * sqrt(2*y) =0 into the second field at http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode and switch the radiobutton to this second field, you get solution including steps, how to find this solution. And another question, why do you write 0.5^2*pi and not simply pi/4 - it is shorter and more convenient for readers. Or do you mean (1/2)^ (2*pi) ? Robert --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Laplace solve:
On 11 lis, 21:53, Jaasiel Ornelas wrote: > Ok. I'm downloading 4.2 to see what happens, otherwise, I'll just do > it by hand. Dous not help, Sage 4.2 cannot solve your equation if you use 0.5 and not 1/2 Change number 0.5 into 1/2 or use Maxima. Robert --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Laplace solve:
Ok. I'm downloading 4.2 to see what happens, otherwise, I'll just do
it by hand.
On Nov 11, 12:13 pm, David Joyner wrote:
> On Wed, Nov 11, 2009 at 3:10 PM, Jaasiel Ornelas wrote:
>
> > I'm using:
>
> > Sage Version 4.1.1, Release Date: 2009-08-14
>
> Okay. The above was done with Sage 4.2, so may or may not work in your
> version.
>
>
>
> > We just started laplace in my class, so I did not know that laplace
> > transforms don't solve non linear ode's. Sorry :p
>
> > On Nov 11, 12:01 pm, David Joyner wrote:
> >> On Wed, Nov 11, 2009 at 1:19 PM, Jaasiel Ornelas
> >> wrote:
>
> >> > I can't get desolve_laplace to give me a good output. I had already
> >> > tried the regular solve (desolve) and it gave to told me that it
> >> > cannot solve that equation. This is my code:
>
> >> > sage: (g,t) = var('g,t')
>
> >> > sage: y=function('y',t)
>
> >> > sage: DEiii = pi * (39/100*y + 1/2)^2* diff(y,t) + a * sqrt(2*g*y)
>
> >> This is a non-linear ODE. You can't use Laplace transforms
> >> to solve such ODEs.
>
> >> However, it is separable and I can solve a slightly simpler version:
>
> >> sage: t = var("t")
> >> sage: y = function("y",t)
> >> sage: DE = y^2*diff(y,t)+sqrt(y)==0
> >> sage: desolve(DE,[y,t])
> >> -2/5*y(t)^(5/2) == c + t
>
> >> Which version of Sage are you using?
>
> >> > sage: a = .5^2*pi
>
> >> > sage: DEiii
>
> >> > 1/1*(39*y(t) + 50)^2*pi*D[0](y)(t) + 0.250*pi*sqrt(g*y
> >> > (t))*sqrt(2)
>
> >> > sage: desolve(DEiii, [y,t])
> >> > Traceback (most recent call last):
> >> > ...
> >> > NotImplementedError: Maxima was unable to solve this system.
>
> >> > sage: desolve_laplace(DEiii, ["t","y"], [0,50,0])
> >> > "?%ilt(-(1521*'laplace('y(t)^2*'diff('y(t),t,1),t,false)+3900*'laplace
> >> > ('y(t)*'diff('y(t),t,1),t,false)+2500*sqrt(2)*'laplace(sqrt(g*'y
> >> > (t)),t,false)-125000)/(2500*false),false,t)"
>
> >> > Perhaps it's because I can't understand the output, but if anyone
> >> > could help me with this, thank you.
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[sage-support] Re: Laplace solve:
As you pointed out, the equation has separated variables, so it must
work allmost in any version
Perhaps problems with keepfloat:true. Is you replace 0.5 by 1/2,
everything works.
See below
Robert
[ma...@um-bc107 /opt/sage]$ ./sage
--
| Sage Version 4.2.1.alpha0, Release Date: 2009-11-09|
| Type notebook() for the GUI, and license() for information.|
--
**
**
* Warning: this is a prerelease version, and it may be unstable. *
**
**
Loading Sage library. Current Mercurial branch is: inequality
sage: (g,t) = var('g,t')
sage: y=function('y',t)
sage: a = (1/2)^2*pi
sage: DEiii = pi * (39/100*y + 1/2)^2* diff(y,t) + a * sqrt(2*g*y)
sage: DEiii
1/1*(39*y(t) + 50)^2*pi*D[0](y)(t) + 1/4*pi*sqrt(g*y(t))*sqrt(2)
sage: desolve(DEiii, [y,t])
-1/12500*(1521*y(t)^2 + 6500*y(t) + 12500)*sqrt(g*y(t))*sqrt(2)/g == c
+ t
sage:
On 11 lis, 21:13, David Joyner wrote:
> On Wed, Nov 11, 2009 at 3:10 PM, Jaasiel Ornelas wrote:
>
> > I'm using:
>
> > Sage Version 4.1.1, Release Date: 2009-08-14
>
> Okay. The above was done with Sage 4.2, so may or may not work in your
> version.
>
>
>
> > We just started laplace in my class, so I did not know that laplace
> > transforms don't solve non linear ode's. Sorry :p
>
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[sage-support] Re: Laplace solve:
On Wed, Nov 11, 2009 at 3:10 PM, Jaasiel Ornelas wrote:
>
> I'm using:
>
> Sage Version 4.1.1, Release Date: 2009-08-14
Okay. The above was done with Sage 4.2, so may or may not work in your version.
>
> We just started laplace in my class, so I did not know that laplace
> transforms don't solve non linear ode's. Sorry :p
>
> On Nov 11, 12:01 pm, David Joyner wrote:
>> On Wed, Nov 11, 2009 at 1:19 PM, Jaasiel Ornelas
>> wrote:
>>
>> > I can't get desolve_laplace to give me a good output. I had already
>> > tried the regular solve (desolve) and it gave to told me that it
>> > cannot solve that equation. This is my code:
>>
>> > sage: (g,t) = var('g,t')
>>
>> > sage: y=function('y',t)
>>
>> > sage: DEiii = pi * (39/100*y + 1/2)^2* diff(y,t) + a * sqrt(2*g*y)
>>
>> This is a non-linear ODE. You can't use Laplace transforms
>> to solve such ODEs.
>>
>> However, it is separable and I can solve a slightly simpler version:
>>
>> sage: t = var("t")
>> sage: y = function("y",t)
>> sage: DE = y^2*diff(y,t)+sqrt(y)==0
>> sage: desolve(DE,[y,t])
>> -2/5*y(t)^(5/2) == c + t
>>
>> Which version of Sage are you using?
>>
>>
>>
>> > sage: a = .5^2*pi
>>
>> > sage: DEiii
>>
>> > 1/1*(39*y(t) + 50)^2*pi*D[0](y)(t) + 0.250*pi*sqrt(g*y
>> > (t))*sqrt(2)
>>
>> > sage: desolve(DEiii, [y,t])
>> > Traceback (most recent call last):
>> > ...
>> > NotImplementedError: Maxima was unable to solve this system.
>>
>> > sage: desolve_laplace(DEiii, ["t","y"], [0,50,0])
>> > "?%ilt(-(1521*'laplace('y(t)^2*'diff('y(t),t,1),t,false)+3900*'laplace
>> > ('y(t)*'diff('y(t),t,1),t,false)+2500*sqrt(2)*'laplace(sqrt(g*'y
>> > (t)),t,false)-125000)/(2500*false),false,t)"
>>
>> > Perhaps it's because I can't understand the output, but if anyone
>> > could help me with this, thank you.
> >
>
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[sage-support] Re: Laplace solve:
I'm using:
Sage Version 4.1.1, Release Date: 2009-08-14
We just started laplace in my class, so I did not know that laplace
transforms don't solve non linear ode's. Sorry :p
On Nov 11, 12:01 pm, David Joyner wrote:
> On Wed, Nov 11, 2009 at 1:19 PM, Jaasiel Ornelas wrote:
>
> > I can't get desolve_laplace to give me a good output. I had already
> > tried the regular solve (desolve) and it gave to told me that it
> > cannot solve that equation. This is my code:
>
> > sage: (g,t) = var('g,t')
>
> > sage: y=function('y',t)
>
> > sage: DEiii = pi * (39/100*y + 1/2)^2* diff(y,t) + a * sqrt(2*g*y)
>
> This is a non-linear ODE. You can't use Laplace transforms
> to solve such ODEs.
>
> However, it is separable and I can solve a slightly simpler version:
>
> sage: t = var("t")
> sage: y = function("y",t)
> sage: DE = y^2*diff(y,t)+sqrt(y)==0
> sage: desolve(DE,[y,t])
> -2/5*y(t)^(5/2) == c + t
>
> Which version of Sage are you using?
>
>
>
> > sage: a = .5^2*pi
>
> > sage: DEiii
>
> > 1/1*(39*y(t) + 50)^2*pi*D[0](y)(t) + 0.250*pi*sqrt(g*y
> > (t))*sqrt(2)
>
> > sage: desolve(DEiii, [y,t])
> > Traceback (most recent call last):
> > ...
> > NotImplementedError: Maxima was unable to solve this system.
>
> > sage: desolve_laplace(DEiii, ["t","y"], [0,50,0])
> > "?%ilt(-(1521*'laplace('y(t)^2*'diff('y(t),t,1),t,false)+3900*'laplace
> > ('y(t)*'diff('y(t),t,1),t,false)+2500*sqrt(2)*'laplace(sqrt(g*'y
> > (t)),t,false)-125000)/(2500*false),false,t)"
>
> > Perhaps it's because I can't understand the output, but if anyone
> > could help me with this, thank you.
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[sage-support] Re: Laplace solve:
On Wed, Nov 11, 2009 at 1:19 PM, Jaasiel Ornelas wrote:
>
> I can't get desolve_laplace to give me a good output. I had already
> tried the regular solve (desolve) and it gave to told me that it
> cannot solve that equation. This is my code:
>
> sage: (g,t) = var('g,t')
>
> sage: y=function('y',t)
>
> sage: DEiii = pi * (39/100*y + 1/2)^2* diff(y,t) + a * sqrt(2*g*y)
This is a non-linear ODE. You can't use Laplace transforms
to solve such ODEs.
However, it is separable and I can solve a slightly simpler version:
sage: t = var("t")
sage: y = function("y",t)
sage: DE = y^2*diff(y,t)+sqrt(y)==0
sage: desolve(DE,[y,t])
-2/5*y(t)^(5/2) == c + t
Which version of Sage are you using?
>
> sage: a = .5^2*pi
>
> sage: DEiii
>
> 1/1*(39*y(t) + 50)^2*pi*D[0](y)(t) + 0.250*pi*sqrt(g*y
> (t))*sqrt(2)
>
> sage: desolve(DEiii, [y,t])
> Traceback (most recent call last):
> ...
> NotImplementedError: Maxima was unable to solve this system.
>
> sage: desolve_laplace(DEiii, ["t","y"], [0,50,0])
> "?%ilt(-(1521*'laplace('y(t)^2*'diff('y(t),t,1),t,false)+3900*'laplace
> ('y(t)*'diff('y(t),t,1),t,false)+2500*sqrt(2)*'laplace(sqrt(g*'y
> (t)),t,false)-125000)/(2500*false),false,t)"
>
> Perhaps it's because I can't understand the output, but if anyone
> could help me with this, thank you.
> >
>
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[sage-support] Re: Laplace solve:
kcrisman writes: > Of course, it would be worth seeing whether one of the other CASs can > solve this one exactly. possibly FriCAS can, it seems: (2) -> DEiii := %pi * (39/100*y t+ 1/2)^2* D(y t,t) + a * sqrt(2*g*y t) 2 , +---+ (1521%pi y(t) + 3900%pi y(t) + 2500%pi)y (t) + 1a\|2g y(t) (2) 1 Type: Expression(Integer) (3) -> solve(DEiii, y, t) +---+ 32 5a t\|2g y(t) + 3042%pi y(t) + 13000%pi y(t) + 25000%pi y(t) (3) --- ++ 5\|y(t) Type: Union(Expression(Integer),...) But WARNING: I did not check the solution and I did not read the manual :-) Martin --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Laplace solve:
> sage: desolve_laplace(DEiii, ["t","y"], [0,50,0])
> "?%ilt(-(1521*'laplace('y(t)^2*'diff('y(t),t,1),t,false)+3900*'laplace
> ('y(t)*'diff('y(t),t,1),t,false)+2500*sqrt(2)*'laplace(sqrt(g*'y
> (t)),t,false)-125000)/(2500*false),false,t)"
>
Looks like yet another Maxima expression we'll need to build into
Sage:
?%ilt
must be a nounform for inverse laplace transform that Maxima can't
give a closed form for. I'm mystified by the "false" stuff, though -
David J. or Robert M., you guys understand the Maxima desolvers, any
ideas?
Of course, it would be worth seeing whether one of the other CASs can
solve this one exactly.
- kcrisman
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