Help with simplifing an equation in terms of 2 variables

1. The problem statement, all variables and given/known data



Hey. I need help simplifying and factoring a differential equation in terms of v and p (velocity(xdot) and position(x) respectively). I need the final answer to be in this form:

a = ( )v + ( )p.

This is so i can put the governing equation in a state-space and eventually use it as a TF and manipulate it for a 2D system.



Definitions:

m = mass

a = acceleration = xdotdot

v = velocity = xdot

p = position = x

b = constant

k = constant

c = constant



2. Relevant equations



ma + (bv + kp) = ((cv)/(v^2 + p^2)^.5))



3. The attempt at a solution



a = (-bv*((v^2+p^2)^.5)-kp*((v^2+p^2)^.5)+cv) / (m*((v^2+p^2)^.5))