How Can I Solve for B as a Function of r in This Equation?

[off-diagonal]

Homework Statement

I've got B as a function of r B[r] B'[r] for derivative B[r] with respect to r and C for constant

Homework Equations

$$\mathbf{\frac{\ B'[r]}{\ r B[r]^2}}+\mathbf{\frac{\ (B[r]-1)}{\ r^2 B[r]}}= C$$

solve for B as a function of r

The Attempt at a Solution

I try to separate r from B[r] term and move it to the other side of the equation and then integrate out but I can't separate them since they are couple to each other.

 

[mighty2000]

I understand your struggle in trying to separate the r and B[r] terms in the given equation. However, there are a few techniques that you can use to solve this problem. One way is to use the substitution method, where you replace B[r] with a new variable, say u, and then solve for u. Once you have the solution for u, you can then substitute back B[r] to get the final solution.

Another technique is to use the power series method, where you expand B[r] into a series of powers of r and then solve for the coefficients. This method requires some algebraic manipulation and may be a bit more complex, but it can also yield a solution.

Lastly, you can also try to use numerical methods to solve for B[r]. This involves using a computer program or a calculator to approximate the solution. This method is useful when the equation cannot be solved analytically.

I hope these suggestions will help you in solving the given equation. Keep in mind that there may be multiple ways to approach this problem, so don't be afraid to try different methods. Good luck!