Algebra with a little differenentation

[munkifisht]

I have the following terms
X, Y, Z, J and K
Where everything is a function of t

I want to combine these equations into a single equation where the X, Y, and Z terms are no longer in the equation and there are only terms of J on the RHS and K on the LHS or visa versa

i) X = Y^2 + Y
ii) Z = dX/dt
iii) J = Z + Y
iv) K = X + J

I'm told this should be possible but not matter which way I combine these I get something along the lines of

K = J^2 + ( K'(t) + J'(t) )^2 - 2*J ( K'(t) + J'(t) ) - ( K'(t)+J'(t) )

and obviously this is going to leave you with products of J and Ks that can't be separated (I need all the K'(t) terms to be over with it's buddy on the LHS). No matter what stratagy I use to avoid this I can't help but get these terms combining.

 

[algebrat]

I want to combine these equations into a single equation where the X, Y, and Z terms are no longer in the equation and there are only terms of J on the RHS and K on the LHS or visa versa...

Where did this problem arise?

I'm told this should be possible...

Who told you this is possible?

 

[munkifisht]

It's a simplification of an RCR electrical circiut problem with a variable resistor that varies as a function of the current. It was an assignment. I've asked and I know the first part is correct.