How to simplify an equation?

Hello,

I have the following problem. There are known dependencies between variables.

The desired quantity is d. In this simple case it can be easily expressed using C1, C2, C, d1, d2. The solution is following

But I am confused with the similar, but a bit more complex problem.

The known dependencies between variables are following

t - time index.

The desired quantity is .

The goal is to express

using C1, C2, C, d1, d2, a1 and a2. The solution of the equation seems cumbersome. Is it possible to reduce the resulting formula to elegant form, which would resemble ?

Re: How to simplify an equation?

Hey tabibito.

Does t have a range (i.e. is it say greater than zero)?

If it does, then expand everything out in terms of C1_0 and C2_0 and given these expressions see if you can use a simplification much like the one you used above.

Also does d_t depend on the time t or is constant across all values of time?

Re: How to simplify an equation?

Thank you for the reply, Chiro. t>0. It can be a fraction, say, 1/12 or 1/2 etc.

d_t depends on C1_t-1, C2_t-1, C_t-1, d1_t, d2_t, a1_t and a2_t. As these variables are time-dependent, d_t will also change with time.

I tried replacements, but it seems that the equation resists simplification.

Re: How to simplify an equation?

Sorry. I mistyped in the first post

It should be