I am trying to symbolically solve for 'ws' in the following equations:

Code:

```
syms N ep es ws
t1=ep*es; t1_=sqrt(1-t1^2); t2=1/ws; t2_=sqrt(1-t2^2);
e1=0.5*(1-t1_^0.5)/(1+t1_^0.5); e2=0.5*(1-t2_^0.5)/(1+t2_^0.5);
q1=e1+2*e1^5; q2=e2+2*e2^5;
K1=pi/2*(1+2*q1+2*q1^4)^2; K2=pi/2*(1+2*q2+2*q2^4)^2;
K1_=K1/pi*log(1/q1); K2_=K2/pi*log(1/q2);
k=N*K1/K1_;
```

Code:

```
solve(k-K2/K2_,ws)
ans =
1/((z^2 + 1)^(1/2)*(1 - z)^(1/2)*(z + 1)^(1/2))
-1/((z^2 + 1)^(1/2)*(1 - z)^(1/2)*(z + 1)^(1/2))
```

Also, I tried simplifying the equations, willingly accepting less precision in favor of a clear answer:

Code:

```
q1=e1; q2=e2;
K1=pi/2*(1+2*q1)^2; K2=pi/2*(1+2*q2)^2;
K1_=K1/pi*log(1/q1); K2_=K2/pi*log(1/q2);
k=N*K1/K1_;
```

Regards,

Vlad.