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#51 2013-12-12 06:40:43

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Wronskian use identities !

But the Wronkian should be nonzero..So,what do I have to do??

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#52 2013-12-12 06:43:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Wronskian use identities !

I do not know why it should be non zero.

Did you compute the Wronskian?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#53 2013-12-12 06:48:00

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Wronskian use identities !

bobbym wrote:

I do not know why it should be non zero.

Did you compute the Wronskian?

Because there is a theorem that says that if two solutions of a differential equation are linearly independent,their Wronskian is nonzero!!!

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#54 2013-12-12 06:54:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Wronskian use identities !

How do you know the two solutions are linearly independent?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#55 2013-12-12 07:57:13

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Wronskian use identities !

bobbym wrote:

How do you know the two solutions are linearly independent?

Because the exercise says that v1,v2 are solutions of the differential equation so that

is not constant..So,
.So,
... hmm

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#56 2013-12-12 08:13:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Wronskian use identities !

That is true but have you used the solutions to compute the wronskian?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#57 2013-12-12 08:37:03

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Wronskian use identities !

bobbym wrote:

That is true but have you used the solutions to compute the wronskian?

Can't I just write that the Wronskian is equal to:
| v_{1}(0)  (v_{1}(0))'  |
| v_{2}(0)  (v_{2}(0))'  |

Do you mean that I have to solve the differential equation that is given for

and
?

Last edited by evinda (2013-12-12 08:37:26)

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#58 2013-12-12 10:52:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Wronskian use identities !

Of course you do, but you already got the solution to DE earlier.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#59 2013-12-13 09:37:07

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Wronskian use identities !

bobbym wrote:

Of course you do, but you already got the solution to DE earlier.

But then don't we find that v1(x)=v2(x) ? Or not? I haven't understood...

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#60 2013-12-13 09:54:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Wronskian use identities !

That is what I am saying. If there is only one solution. Is there another solution?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#61 2013-12-13 11:18:19

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Wronskian use identities !

bobbym wrote:

That is what I am saying. If there is only one solution. Is there another solution?

There should be..because v1 and v2 are linearly independent hmm

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#62 2013-12-13 11:20:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Wronskian use identities !

What is the other solution?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#63 2013-12-13 11:26:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: Wronskian use identities !

There are infinitely many solutions.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#64 2013-12-13 11:29:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: Wronskian use identities !

Yes but when you plug them into that determinant they are going to become 0.

We have no particular solution just a 1 general one. To continue with this route he will need 2 different general solutions.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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