Ordinary Differential equation

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

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

where v is velocity and g is a gravitational constant

show that by making the substitution $\displaystyle u = v^2$ we obtain

$\displaystyle {du}/{dx} + (^{2}/_{x+1})u=2(^{x-1}/_{x+2})g$

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!.