I have 2 equations with two variables $x,y$ that need to be solved. I'm so sure it can be done, but when I try going about it, I hit a wall and just don't know what to do. I also have MATLAB at my disposal, so if anyone has a resource that can solve them with that, that's an option too!
Here's the equations in question:
$$ \dfrac{-2A}{x^{13}}+\dfrac{B}{x^7} + \dfrac{-2A}{(x-y)^{13}}+\dfrac{B}{(x-y)^7}=0 $$ $$ \dfrac{-2A}{y^{13}}+\dfrac{B}{y^7} + \dfrac{2A}{(x-y)^{13}}+\dfrac{-B}{(x-y)^7}=0 $$
We assume that $A,B$ are constants.
I found at least one solution. Suppose that $y=-x$. Then the two equations reduce to a single equation:
$$ -\frac{2A}{x^{13}}+\frac{B}{x^7}-\frac{2A}{2^{13}x^{13}}+\frac{B}{2^7x^7}=0. $$ Multiplying by $x^{13}$: $$ -2A(1+2^{-13})+Bx^6(1+2^{-7})=0. $$ Hence, $x^6=\frac{2A(1+2^{-13})}{B(1+2^{-7})}$. This is approximately $2A/B$.