Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,896

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

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

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!!!

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,896

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

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

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, ...

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,896

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

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

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)*

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,896

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.**

Offline

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

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...

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,896

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.**

Offline

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

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,896

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.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

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.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,896

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.**

Offline