2 equations. How to find X°/X?

[beaf123]

Homework Statement

I have two equations.

1. b(N) = rN^k

2. bN° = Y - X - C

How can I find an expression for N°/N

Homework Equations

The Attempt at a Solution

I am a little lost here since I don't 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 don't 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.

 

[Mark44]

Homework Statement

I have two equations.

1. b(N) = rN^k

2. bN° = Y - X - C

What is N° supposed to mean?
I read your explanation below, but I still don't understand what you mean.

How can I find an expression for N°/N

Homework Equations

The Attempt at a Solution

I am a little lost here since I don't 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 don't 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.

Why not call it b'(N)? Differentiation both sides with respect to N would give b'(N) = rkN^{k - 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?

 

[Ray Vickson]

Homework Statement

I have two equations.

1. b(N) = rN^k

2. bN° = Y - X - C

How can I find an expression for N°/N

Homework Equations

The Attempt at a Solution

I am a little lost here since I don't 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 don't 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.

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 $dX/dt$?

Please try to submit complete and readable questions, using standard notation.

 

[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 don't really expect an answer here because I still think my post is not good enough. And also I can't 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.