我想在MATLAB中求解此方程。通过数值解算器，我知道某些根是虚构的，而另一些是真实的。通过使用Solve，MATLAB会列出解决方案有效的条件列表。
我只希望MATLAB用解析解决方案解决此问题（不是数值方法，我可以在Mathematica中做到这一点）。有更好的解决方案，还是我可以使用的任何其他软件包？
syms f2 ep1 ep2 a1 a2 fp1 fp2 h e1 m1 mp R f r t1 f1
eqn = (((ep2*fp1 - ep1*fp2)*mp*(e1*m1*(ep2*f2*fp1*(fp2 - a2*mp) +...
ep1*fp2*(-(f1*fp2) + a2*f2*mp))*(h + R) + a2*f2*(-(ep2*f*f2*fp1*R)+...
ep1*f*f1*fp2*R - ...
ep1*ep2*(f1 - f2)*mp*r*(h + R)))* (a1*ep1*ep2*f1*(f1 - f2)...
*mp*(ep2*f*f2*fp1*R - ep1*f*f1*fp2*R + ep1*ep2*(f1 - f2)*mp*r*(h + R)) +...
e1*(ep2^2*f*f2^2*fp1^2*R*t1 + ...
ep1^2*f1*fp2*(f*f1*fp2*R*t1 - ep2*(f1 - f2)*mp*(h + R)*(-(fp1*m1) + ...
a1*m1*mp + r*t1)) + ...
ep1*ep2*fp1*(-2*f*f1*f2*fp2*R*t1 + ep2*(f1 - f2)*mp*(h + R)*(-(f2*fp1*m1)+...
a1*f1*m1*mp + f2*r*t1)))))/...
(e1*ep1*ep2*(ep2*f2*fp1 - ep1*f1*fp2)^2*(h + R)^2*(ep1*ep2*(f1 - f2)*...
(-(a2*f2*fp1) + a1*f1*fp2)*mp + e1*(ep2*f2*fp1*(fp2 - a2*mp) + ...
ep1*fp2*(-(f1*fp2) + a2*f2*mp))*t1))) * (-1) == 0;
solve(eqn,fp1)
The solutions I get are:
(a2*f2*(R*ep1*f*f1*fp2 - ep1*ep2*mp*r*(R + h)*(f1 - f2)) - e1*ep1*fp2*m1*(R + h)*(f1*fp2 - a2*f2*mp))/(R*a2*ep2*f*f2^2 - e1*ep2*m1*(R + h)*(fp2 - a2*mp)*f2)
(ep1*fp2)/ep2
(ep1*f1*mp*(R^2*a1^2*e1^2*ep2^2*f1^2*m1^2*mp^2 + 2*R^2*a1^2*e1*ep2^2*f*f1^2*f2*m1*mp + R^2*a1^2*ep2^2*f^2*f1^2*f2^2 + 2*R^2*a1*e1^2*ep1*ep2*f1^2*fp2*m1^2*mp - 4*R^2*a1*e1^2*ep1*ep2*f1*f2*fp2*m1^2*mp + 2*R^2*a1*e1^2*ep2^2*f1*f2*m1*mp*r*t1 - 4*R^2*a1*e1^2*ep2*f*f1*f2*fp2*m1*t1 + 4*R^2*a1*e1*ep1*ep2^2*f1^2*f2*m1*mp*r - 4*R^2*a1*e1*ep1*ep2^2*f1*f2^2*m1*mp*r - 2*R^2*a1*e1*ep1*ep2*f*f1^2*f2*fp2*m1 - 2*R^2*a1*e1*ep2^2*f*f1*f2^2*r*t1 + R^2*e1^2*ep1^2*f1^2*fp2^2*m1^2 - 2*R^2*e1^2*ep1*ep2*f1*f2*fp2*m1*r*t1 + R^2*e1^2*ep2^2*f2^2*r^2*t1^2 + 2*R*a1^2*e1^2*ep2^2*f1^2*h*m1^2*mp^2 + 2*R*a1^2*e1*ep2^2*f*f1^2*f2*h*m1*mp + 4*R*a1*e1^2*ep1*ep2*f1^2*fp2*h*m1^2*mp - 8*R*a1*e1^2*ep1*ep2*f1*f2*fp2*h*m1^2*mp + 4*R*a1*e1^2*ep2^2*f1*f2*h*m1*mp*r*t1 - 4*R*a1*e1^2*ep2*f*f1*f2*fp2*h*m1*t1 + 8*R*a1*e1*ep1*ep2^2*f1^2*f2*h*m1*mp*r - 8*R*a1*e1*ep1*ep2^2*f1*f2^2*h*m1*mp*r - 2*R*a1*e1*ep1*ep2*f*f1^2*f2*fp2*h*m1 - 2*R*a1*e1*ep2^2*f*f1*f2^2*h*r*t1 + 2*R*e1^2*ep1^2*f1^2*fp2^2*h*m1^2 - 4*R*e1^2*ep1*ep2*f1*f2*fp2*h*m1*r*t1 +\\\r\n 2*R*e1^2*ep2^2*f2^2*h*r^2*t1^2 + a1^2*e1^2*ep2^2*f1^2*h^2*m1^2*mp^2 + 2*a1*e1^2*ep1*ep2*f1^2*fp2*h^2*m1^2*mp - 4*a1*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1^2*mp + 2*a1*e1^2*ep2^2*f1*f2*h^2*m1*mp*r*t1 + 4*a1*e1*ep1*ep2^2*f1^2*f2*h^2*m1*mp*r - 4*a1*e1*ep1*ep2^2*f1*f2^2*h^2*m1*mp*r + e1^2*ep1^2*f1^2*fp2^2*h^2*m1^2 - 2*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1*r*t1 + e1^2*ep2^2*f2^2*h^2*r^2*t1^2)^(1/2) - ep1*f2*mp*(R^2*a1^2*e1^2*ep2^2*f1^2*m1^2*mp^2 + 2*R^2*a1^2*e1*ep2^2*f*f1^2*f2*m1*mp + R^2*a1^2*ep2^2*f^2*f1^2*f2^2 + 2*R^2*a1*e1^2*ep1*ep2*f1^2*fp2*m1^2*mp - 4*R^2*a1*e1^2*ep1*ep2*f1*f2*fp2*m1^2*mp + 2*R^2*a1*e1^2*ep2^2*f1*f2*m1*mp*r*t1 - 4*R^2*a1*e1^2*ep2*f*f1*f2*fp2*m1*t1 + 4*R^2*a1*e1*ep1*ep2^2*f1^2*f2*m1*mp*r - 4*R^2*a1*e1*ep1*ep2^2*f1*f2^2*m1*mp*r - 2*R^2*a1*e1*ep1*ep2*f*f1^2*f2*fp2*m1 - 2*R^2*a1*e1*ep2^2*f*f1*f2^2*r*t1 + R^2*e1^2*ep1^2*f1^2*fp2^2*m1^2 - 2*R^2*e1^2*ep1*ep2*f1*f2*fp2*m1*r*t1 + R^2*e1^2*ep2^2*f2^2*r^2*t1^2 + 2*R*a1^2*e1^2*ep2^2*f1^2*h*m1^2*mp^2 + 2*R*a1^2*e1*ep2^2*f*f1^2*f2*h*m1*mp + 4*R*a\\\r\n1*e1^2*ep1*ep2*f1^2*fp2*h*m1^2*mp - 8*R*a1*e1^2*ep1*ep2*f1*f2*fp2*h*m1^2*mp + 4*R*a1*e1^2*ep2^2*f1*f2*h*m1*mp*r*t1 - 4*R*a1*e1^2*ep2*f*f1*f2*fp2*h*m1*t1 + 8*R*a1*e1*ep1*ep2^2*f1^2*f2*h*m1*mp*r - 8*R*a1*e1*ep1*ep2^2*f1*f2^2*h*m1*mp*r - 2*R*a1*e1*ep1*ep2*f*f1^2*f2*fp2*h*m1 - 2*R*a1*e1*ep2^2*f*f1*f2^2*h*r*t1 + 2*R*e1^2*ep1^2*f1^2*fp2^2*h*m1^2 - 4*R*e1^2*ep1*ep2*f1*f2*fp2*h*m1*r*t1 + 2*R*e1^2*ep2^2*f2^2*h*r^2*t1^2 + a1^2*e1^2*ep2^2*f1^2*h^2*m1^2*mp^2 + 2*a1*e1^2*ep1*ep2*f1^2*fp2*h^2*m1^2*mp - 4*a1*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1^2*mp + 2*a1*e1^2*ep2^2*f1*f2*h^2*m1*mp*r*t1 + 4*a1*e1*ep1*ep2^2*f1^2*f2*h^2*m1*mp*r - 4*a1*e1*ep1*ep2^2*f1*f2^2*h^2*m1*mp*r + e1^2*ep1^2*f1^2*fp2^2*h^2*m1^2 - 2*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1*r*t1 + e1^2*ep2^2*f2^2*h^2*r^2*t1^2)^(1/2) - R*e1*ep1^2*f1^2*fp2*m1*mp - e1*ep1^2*f1^2*fp2*h*m1*mp + e1*ep1*ep2*f2^2*h*mp*r*t1 - R*a1*e1*ep1*ep2*f1^2*m1*mp^2 - a1*e1*ep1*ep2*f1^2*h*m1*mp^2 + 2*R*e1*ep1*f*f1*f2*fp2*t1 + R*a1*ep1*ep2*f*f1*f2^2*mp - R*a1*ep1*ep2*f*f1^2*f2*mp + R*e1\\\r\n*ep1^2*f1*f2*fp2*m1*mp + R*e1*ep1*ep2*f2^2*mp*r*t1 + e1*ep1^2*f1*f2*fp2*h*m1*mp - R*e1*ep1*ep2*f1*f2*mp*r*t1 - e1*ep1*ep2*f1*f2*h*mp*r*t1 + R*a1*e1*ep1*ep2*f1*f2*m1*mp^2 + a1*e1*ep1*ep2*f1*f2*h*m1*mp^2)/(2*e1*ep2*f2*(R*f*f2*t1 - R*ep1*f1*m1*mp + R*ep1*f2*m1*mp - ep1*f1*h*m1*mp + ep1*f2*h*m1*mp))
(ep1*f2*mp*(R^2*a1^2*e1^2*ep2^2*f1^2*m1^2*mp^2 + 2*R^2*a1^2*e1*ep2^2*f*f1^2*f2*m1*mp + R^2*a1^2*ep2^2*f^2*f1^2*f2^2 + 2*R^2*a1*e1^2*ep1*ep2*f1^2*fp2*m1^2*mp - 4*R^2*a1*e1^2*ep1*ep2*f1*f2*fp2*m1^2*mp + 2*R^2*a1*e1^2*ep2^2*f1*f2*m1*mp*r*t1 - 4*R^2*a1*e1^2*ep2*f*f1*f2*fp2*m1*t1 + 4*R^2*a1*e1*ep1*ep2^2*f1^2*f2*m1*mp*r - 4*R^2*a1*e1*ep1*ep2^2*f1*f2^2*m1*mp*r - 2*R^2*a1*e1*ep1*ep2*f*f1^2*f2*fp2*m1 - 2*R^2*a1*e1*ep2^2*f*f1*f2^2*r*t1 + R^2*e1^2*ep1^2*f1^2*fp2^2*m1^2 - 2*R^2*e1^2*ep1*ep2*f1*f2*fp2*m1*r*t1 + R^2*e1^2*ep2^2*f2^2*r^2*t1^2 + 2*R*a1^2*e1^2*ep2^2*f1^2*h*m1^2*mp^2 + 2*R*a1^2*e1*ep2^2*f*f1^2*f2*h*m1*mp + 4*R*a1*e1^2*ep1*ep2*f1^2*fp2*h*m1^2*mp - 8*R*a1*e1^2*ep1*ep2*f1*f2*fp2*h*m1^2*mp + 4*R*a1*e1^2*ep2^2*f1*f2*h*m1*mp*r*t1 - 4*R*a1*e1^2*ep2*f*f1*f2*fp2*h*m1*t1 + 8*R*a1*e1*ep1*ep2^2*f1^2*f2*h*m1*mp*r - 8*R*a1*e1*ep1*ep2^2*f1*f2^2*h*m1*mp*r - 2*R*a1*e1*ep1*ep2*f*f1^2*f2*fp2*h*m1 - 2*R*a1*e1*ep2^2*f*f1*f2^2*h*r*t1 + 2*R*e1^2*ep1^2*f1^2*fp2^2*h*m1^2 - 4*R*e1^2*ep1*ep2*f1*f2*fp2*h*m1*r*t1 +\\\r\n 2*R*e1^2*ep2^2*f2^2*h*r^2*t1^2 + a1^2*e1^2*ep2^2*f1^2*h^2*m1^2*mp^2 + 2*a1*e1^2*ep1*ep2*f1^2*fp2*h^2*m1^2*mp - 4*a1*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1^2*mp + 2*a1*e1^2*ep2^2*f1*f2*h^2*m1*mp*r*t1 + 4*a1*e1*ep1*ep2^2*f1^2*f2*h^2*m1*mp*r - 4*a1*e1*ep1*ep2^2*f1*f2^2*h^2*m1*mp*r + e1^2*ep1^2*f1^2*fp2^2*h^2*m1^2 - 2*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1*r*t1 + e1^2*ep2^2*f2^2*h^2*r^2*t1^2)^(1/2) - ep1*f1*mp*(R^2*a1^2*e1^2*ep2^2*f1^2*m1^2*mp^2 + 2*R^2*a1^2*e1*ep2^2*f*f1^2*f2*m1*mp + R^2*a1^2*ep2^2*f^2*f1^2*f2^2 + 2*R^2*a1*e1^2*ep1*ep2*f1^2*fp2*m1^2*mp - 4*R^2*a1*e1^2*ep1*ep2*f1*f2*fp2*m1^2*mp + 2*R^2*a1*e1^2*ep2^2*f1*f2*m1*mp*r*t1 - 4*R^2*a1*e1^2*ep2*f*f1*f2*fp2*m1*t1 + 4*R^2*a1*e1*ep1*ep2^2*f1^2*f2*m1*mp*r - 4*R^2*a1*e1*ep1*ep2^2*f1*f2^2*m1*mp*r - 2*R^2*a1*e1*ep1*ep2*f*f1^2*f2*fp2*m1 - 2*R^2*a1*e1*ep2^2*f*f1*f2^2*r*t1 + R^2*e1^2*ep1^2*f1^2*fp2^2*m1^2 - 2*R^2*e1^2*ep1*ep2*f1*f2*fp2*m1*r*t1 + R^2*e1^2*ep2^2*f2^2*r^2*t1^2 + 2*R*a1^2*e1^2*ep2^2*f1^2*h*m1^2*mp^2 + 2*R*a1^2*e1*ep2^2*f*f1^2*f2*h*m1*mp + 4*R*a\\\r\n1*e1^2*ep1*ep2*f1^2*fp2*h*m1^2*mp - 8*R*a1*e1^2*ep1*ep2*f1*f2*fp2*h*m1^2*mp + 4*R*a1*e1^2*ep2^2*f1*f2*h*m1*mp*r*t1 - 4*R*a1*e1^2*ep2*f*f1*f2*fp2*h*m1*t1 + 8*R*a1*e1*ep1*ep2^2*f1^2*f2*h*m1*mp*r - 8*R*a1*e1*ep1*ep2^2*f1*f2^2*h*m1*mp*r - 2*R*a1*e1*ep1*ep2*f*f1^2*f2*fp2*h*m1 - 2*R*a1*e1*ep2^2*f*f1*f2^2*h*r*t1 + 2*R*e1^2*ep1^2*f1^2*fp2^2*h*m1^2 - 4*R*e1^2*ep1*ep2*f1*f2*fp2*h*m1*r*t1 + 2*R*e1^2*ep2^2*f2^2*h*r^2*t1^2 + a1^2*e1^2*ep2^2*f1^2*h^2*m1^2*mp^2 + 2*a1*e1^2*ep1*ep2*f1^2*fp2*h^2*m1^2*mp - 4*a1*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1^2*mp + 2*a1*e1^2*ep2^2*f1*f2*h^2*m1*mp*r*t1 + 4*a1*e1*ep1*ep2^2*f1^2*f2*h^2*m1*mp*r - 4*a1*e1*ep1*ep2^2*f1*f2^2*h^2*m1*mp*r + e1^2*ep1^2*f1^2*fp2^2*h^2*m1^2 - 2*e1^2*ep1*ep2*f1*f2*fp2*h^2*m1*r*t1 + e1^2*ep2^2*f2^2*h^2*r^2*t1^2)^(1/2) - R*e1*ep1^2*f1^2*fp2*m1*mp - e1*ep1^2*f1^2*fp2*h*m1*mp + e1*ep1*ep2*f2^2*h*mp*r*t1 - R*a1*e1*ep1*ep2*f1^2*m1*mp^2 - a1*e1*ep1*ep2*f1^2*h*m1*mp^2 + 2*R*e1*ep1*f*f1*f2*fp2*t1 + R*a1*ep1*ep2*f*f1*f2^2*mp - R*a1*ep1*ep2*f*f1^2*f2*mp + R*e1\\\r\n*ep1^2*f1*f2*fp2*m1*mp + R*e1*ep1*ep2*f2^2*mp*r*t1 + e1*ep1^2*f1*f2*fp2*h*m1*mp - R*e1*ep1*ep2*f1*f2*mp*r*t1 - e1*ep1*ep2*f1*f2*h*mp*r*t1 + R*a1*e1*ep1*ep2*f1*f2*m1*mp^2 + a1*e1*ep1*ep2*f1*f2*h*m1*mp^2)/(2*e1*ep2*f2*(R*f*f2*t1 - R*ep1*f1*m1*mp + R*ep1*f2*m1*mp - ep1*f1*h*m1*mp + ep1*f2*h*m1*mp))