# 2 equations. How to find X°/X?

1. Mar 17, 2015

### beaf123

1. The problem statement, all variables and given/known data
I have two equations.

1. b(N) = rN^k

2. bN° = Y - X - C

How can I find an expression for N°/N

2. Relevant equations

3. The attempt at a solution

I am a little lost here since I dont know much about the properties of differential equations. So my attempts at solution has been to take the derivative of the first equation and call it N°, which I dont know if I am alloved to do. Then insert it into the second equation and solve it for N. It doesent seem to be right.

2. Mar 17, 2015

### Staff: Mentor

What is N° supposed to mean?
I read your explanation below, but I still don't understand what you mean.
Why not call it b'(N)? Differentiation both sides with respect to N would give b'(N) = rkNk - 1, but I don't see that doing this is helpful.

Also, how do x and y tie in here? Your first equation involves N, and what appear to be constants, r and k.

This is very confusing. What is the exact statement of the problem?

3. Mar 17, 2015

### Ray Vickson

Does your mysterious notation $X^o$ mean $\dot{X} = dX(t)/dt$? If so, are you saying that you have
$$\frac{d}{dt} \left( r N^k \right) = Y- X - C?$$
Are $r,k$ constants? Are $N, Y, X,C$ functions of $t$? And, if $X^o$ does mean $dX/dt$, where in your equations is there anything that tells you about $dX/dt$?

4. Mar 18, 2015

### beaf123

The question is from a paper.

They write:

If we substitute the formula for R&D cost from equation 6.36 into the resource constraint 6.23 we get:

6.36

6.23

X and Y

I dont really expect an answer here because I still think my post is not good enough. And also I cant bes sure I have provided you with all the necessary information, but if what they have done is intuitive to any of you and that you understand what they did, I would very much appreciate an answer.

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