Need HELP equation of motion with variable acceleration

[Behroz]

Homework Statement

A particle is dropped from rest, at the surface, into a tank containing oil
The acceleration of the particle in the oil is a = g – kv
where g is the gravitational acceleration and –kv being denoted by
the resistance put on the particle by the oil.
Solve for x as a function of time!

The Attempt at a Solution

I'm attaching an image file containing my calculations.
As can be seen I get a differential equation of the second order
but as I proceed to solve this equation and try to determine the
constants the whole thing turns into ZERO?!? What am I doing wrong??

 

[P3X-018]

You don't need to consider this as a 2. order diff. equation. You can view the equation as

$$\ddot{x} = g - k\dot{x}$$
or
$$\dot{v} = g - kv$$

The second equation is just a 1. order diff. equation with respect to the velocity v.

 

[Behroz]

You don't need to consider this as a 2. order diff. equation. You can view the equation as

$$\ddot{x} = g - k\dot{x}$$
or
$$\dot{v} = g - kv$$

The second equation is just a 1. order diff. equation with respect to the velocity v.

Yeah, you're right.. but one SHOULD be able solve it by puting it up as a second order right? I just want to know what I'm doing wrong, it really bugs me.

 

[denverdoc]

what have you got? Kind of hard to know what's wrong when we just have a generic list of eqns...
John S