Is it possible to solve the following equation analytically?
$B_1\exp(\beta_1 x) + B_2\exp(\beta_2 x) = C_1\exp(\alpha_1 x) + C_2\exp(\alpha_2 x)$
where, $B_1$, $B_2$, $C_1$, $C_2$, $\beta_1$, $\beta_2$, $\alpha_1$ and $\alpha_2$ are constants. And $x$ is the independent variable.
Many many thanks in advance.
No. For example, $1+e^x=e^{2x}+e^{17x}$ becomes $y^{17}+y^2-y-1=0$ on substituting $y=e^x$, a polynomial equation of degree 17. Polynomials of degree exceeding 4 are, in general, not solvable analytically, only numerically.