Solution of a matrix equation: (Ce^{At})(rho_p) + (CA)^{-1} (e^{At} - I) B = 0

[rehan_eme]

I want to know if a second solution exists for the following math equation:
$$Ce^{At} ρ_p+(CA)^{−1} (e^{At}−I)B=0$$Where C, ρ_p, A, and B are constant matrices, 't' is a scalar variable. I know that at least one solution i.e. t=θ_1 exists, but I want a method to determine if there is another $θ_0 <θ_1$ that is also a (second) solution. Any analytical way of determining that is what I am looking for.

 

[Steven G]

Can you share the work you have done so far? This is a help forum which means that we don't provide solutions for students, since that wouldn't be helpful.