differential equation

A point P moves along the x-axis with acceleration away from the origin O inversely proportional to OP = a
So
v=dx/dt
dv/dt=C/x where C is a constant
Combine
d^2x/dt^2=C/x
v(dv/dx)=C/x
(1/C)vdv=dx/x
(1/C)v^2=2lnx
when x=2a,v=V
(1/C)V^2=2ln2a
C=V^2/2ln2a
v=SQRT[V^2lnx/ln2a]
when OP=x=ka
v=SQRT[V^2lnka/ln2a]
v=VSQRT[ln(ka)/ln2a]


2009-01-24 15:57:56 補充：
計不到你的答案

2009-01-24 22:53:08 補充：
我估出錯可能性大些﹐因為連answer book都冇solution

我計到同myisland差不多的答案。問題可能出於inversely proportional到。我試過如果係directly proportional個答案會比較似啲。