Simple question in ODE

**WannaBe** · December 30th 2009, 01:15 AM

Given this ODE :
y'=2*sqrt(|y|) , y(0)=0 ...
Can we find two different soloutions around (0,0) ? If there are, find them... If there are no two different soloutions around (0,0) - explain why...

Help is needed! TNX

**Sudharaka** · December 30th 2009, 02:43 AM

Dear WannaBe,

I need some further details to try this problem. What do you mean by,
y(0)=0 ?

And what is "around (0,0)"?

**WannaBe** · December 30th 2009, 03:13 AM

Hey there Sudharaka,
The problem is an initial value ODE problem. i.e an equation with an initial value condition... In this one, the equation is: y'=2*sqrt(|y|) and the soloution must be a function y(x) that for x=0: y(x)=0 -> y(0)=0...It's just an initial value condition for the equation...

When I say Around (0,0) I mean that:
"Can we find two different soloutions in some neighborhood around (0,0) ?"

Hope you'll be able to help me now... btw-I'll be delighted if you'll be able to help me in the other question I've posted about ODE's...

TNX in advance...

**Sudharaka** · December 30th 2009, 04:37 PM

Dear WannaBe,
Please see the attachment below. From that it is evident that this equation have two solutions for all x values. If you have any problems or if you can't read the attachment please feel free to contact me.

Hope this helps.

**chisigma** · December 31st 2009, 01:10 AM

An initial value problem like this ...

$y^{'} = 2\cdot \sqrt {|y|}$ , $y(0)=0$ (1)

... in general admits a single solution if the so called 'Lipschitz conditions' are satisfied...

Initial value problem - Wikipedia, the free encyclopedia

... what is not the case of (1). If we observe the (1) we note that $y^{'}$ is a function of the $y$ only and that means that if $\varphi(x)$ is solution of (1), then $\varphi(x+\alpha)$ being $\alpha$ an arbitrary constant is also solution of (1). In particular we can observe that solution of (1) is...

$\varphi(x) = x^{2}, x>0$

$\varphi(x)=0, x\le 0$ (2)

... so that any $\varphi (x + \alpha), \alpha<0$ is also solution of (1)...

Kind regards

$\chi$ $\sigma$

**WannaBe** · December 31st 2009, 02:07 AM

TNX a lot!

Thread: Simple question in ODE

LinkBack

Thread Tools

Display

Simple question in ODE

Similar Math Help Forum Discussions

[SOLVED] Really simple question too hard for a simple mind

Easy Question - Simple Interest, Simple Discount

Maths dispute - a very simple simple exponents question

Simple Integral Question (I think it's simple)

Simple function transformation question and cusp question

Search Tags