Ordinary Differential equation

**the_sensai** · December 11th 2008, 11:25 AM

A uniform chain of total length 8 metres, settle 1 metre above the ledge and 2 metres hang on the other side. If x represents the length. The motion of the chain is

$(x+1)v(dv/dx) + v^2 = (x-1)g$

where v is velocity and g is a gravitational constant
show that by making the substitution $u = v^2$ we obtain
${du}/{dx} + (^{2}/_{x+1})u=2(^{x-1}/_{x+2})g$

now do i have to integrate this in order to subsitute?
any help on this would be appreciated as i have no idea where to start cheers people!.

**Mush** · December 11th 2008, 11:37 AM

Why not use an integrating factor?

$\phi (x) = e^{\int p(x)dx}$

$\phi (x) u(x) = \int \phi (x) r(x) dx$

Where

$\frac{du}{dx} + p(x)u = r(x)$

Is the format.

Sorry, the above is what you would do to solve after substitution. You don't need to integrate BEFORE you substitute.

I'm fairly sure your of the latter equation should be $2 (\frac{x-1}{x+1})g$ , no?

If that's the case:

Divide through by $x+1$

After that apply the following considerations:

$u = v^2$

$\frac{du}{dv} = 2v$

$vdv = \frac{1}{2}du$

$\frac{dv}{dx}v = \frac{1}{2}\frac{du}{dx}$

Should help!

**the_sensai** · December 11th 2008, 11:44 AM

brilliant cheers got it!

Thread: Ordinary Differential equation

LinkBack

Thread Tools

Display

Ordinary Differential equation

thanks

Similar Math Help Forum Discussions

Ordinary Differential Equation Help

ordinary differential equation

First order ordinary differential equation

Ordinary Differential Equation

Ordinary Differential Equation

Search Tags