HELP 2nd ODE

d2x/dt2= kv-2

where v = dx/dt, we get dv/dx = dv/dt X dt/dx = 1/v d2x/dt2

So, d2x/dt2= vdv/dx

We can actually rewrite the differential equation into:

vdv/dx = kv-2

∫v3dv = k∫dx

v4/4= kx + c, where c is a constant

v(0) =0, and x(0) = 0, so we have c = 0

v4= 4kx

v = (4kx)1/4= √2 X (kx)1/4



2009-08-21 16:04:26 補充：
Because d2x/dt2 = d/dt(dx/dt)

And v = dx/dt

So, d2x/dt2 = dv/dt