Solve Mechanics Problem: Particle with Mass m and Resistive Force of mkv^2

[thereddevils]

Homework Statement

A particle with mass m is projected vertically upwards from a point with speed u. THe particle, besides being subjected to gravity, experiences a resistive force of magnitude
mkv^2, with v as its velocity when its height from the point of projection is x and k as a positive constant. Show that

$$v^2=(\frac{g}{k}+u^2)e^{-2kx}-\frac{g}{k}$$

Homework Equations

The Attempt at a Solution

F-mkv-mg=ma

using v^2=u^2+2as

v^2=u^2-2gx

thats all i can get

 

[Fightfish]

Did you know that the equation v^2 = u^2 + 2as only holds for constant acceleration? You will have to integrate in this case due to the varying acceleration.

 

[thereddevils]

Did you know that the equation v^2 = u^2 + 2as only holds for constant acceleration? You will have to integrate in this case due to the varying acceleration.

thanks , for this , do i integrate

F-mkv-mg=ma ?

am i supposed to get rid of some of the terms here first before i integrate ?