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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,768

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,768

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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,
...

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,768

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,768

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,768

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #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

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,768

### Re: Wronskian use identities !

What is the other solution?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### 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
The knowledge of some things as a function of age is a delta function.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,768

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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