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 Post subject: 2nd Order Differential Equation + Boundary Conditions!Posted: Thu, 8 Mar 2012 16:37:20 UTC
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Joined: Thu, 8 Mar 2012 14:46:00 UTC
Posts: 4
Hi guys, I have been doing some questions on complex numbers and second order differential equations. It's been going mostly fine, but now I have hit a bit of brick wall in my mind.

The question is this:

Solve the equation:

subject to the boundary conditions y(0) = 0 and y(pi) = 0

I can solve it fine, I get: Ae^-2x + Bxe^-2x + 4/25sinx + 3/25cosx

But I can't get my head around what I am supposed to do with the boundary conditions, I'm completely lost

Does anybody have any ideas? Any help would be great thanks

 Last edited by outermeasure on Fri, 9 Mar 2012 08:12:30 UTC, edited 1 time in total. Replace dead wolframalpha image with TeX

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 Post subject: Re: 2nd Order Differential Equation + Boundary Conditions!Posted: Thu, 8 Mar 2012 16:40:10 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Vespre wrote:
Hi guys, I have been doing some questions on complex numbers and second order differential equations. It's been going mostly fine, but now I have hit a bit of brick wall in my mind.

The question is this:

Solve the equation:

subject to the boundary conditions y(0) = 0 and y(pi) = 0

I can solve it fine, I get: Ae^-2x + Bxe^-2x + 4/25sinx + 3/25cosx

But I can't get my head around what I am supposed to do with the boundary conditions, I'm completely lost

Does anybody have any ideas? Any help would be great thanks

Use the boundary conditions to solve for A and B!

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 Post subject: Re: 2nd Order Differential Equation + Boundary Conditions!Posted: Thu, 8 Mar 2012 16:53:32 UTC
 S.O.S. Newbie

Joined: Thu, 8 Mar 2012 14:46:00 UTC
Posts: 4
I got that bit I'm just not sure how to. Do I sub 0 into the equation somehow? What about the pi one?

If anybody can show me or at least show me a little bit to help get me started, that would be great.

Thanks for the quick reply though

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 Post subject: Re: 2nd Order Differential Equation + Boundary Conditions!Posted: Thu, 8 Mar 2012 16:54:40 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Vespre wrote:
I got that bit I'm just not sure how to. Do I sub 0 into the equation somehow? What about the pi one?

If anybody can show me or at least show me a little bit to help get me started, that would be great.

Thanks for the quick reply though

That's certainly what and mean, right? That's not differential equations, it's definition of how functions work.

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 Post subject: Re: 2nd Order Differential Equation + Boundary Conditions!Posted: Thu, 8 Mar 2012 17:10:03 UTC
 S.O.S. Newbie

Joined: Thu, 8 Mar 2012 14:46:00 UTC
Posts: 4
Well the equation itself is a second order differential, so you solve it with the axillary equation (set it to = 0), then solve the particular integral (right hand side bit) to get the general solution.

It then just asks me to do solve it 'subject to the boundary conditions y(0) = 0 and y(pi) = 0. So I assume it just means set my solved equation to 0 and stick 0 where x is? And for the other one, do the same, but stick pi where x is? And it should give me some values for A and B that I can stick in to give me a fully solved equation?

Sorry if I completely missed your point there, I think I've confused myself more than I needed to

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 Post subject: Re: 2nd Order Differential Equation + Boundary Conditions!Posted: Thu, 8 Mar 2012 21:00:34 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Vespre wrote:
Well the equation itself is a second order differential, so you solve it with the axillary equation (set it to = 0), then solve the particular integral (right hand side bit) to get the general solution.

It then just asks me to do solve it 'subject to the boundary conditions y(0) = 0 and y(pi) = 0. So I assume it just means set my solved equation to 0 and stick 0 where x is? And for the other one, do the same, but stick pi where x is? And it should give me some values for A and B that I can stick in to give me a fully solved equation?

Sorry if I completely missed your point there, I think I've confused myself more than I needed to

He already did those things, he just didn't realize to use the boundary conditions.

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