We're given this equation and told to find the value of $A$.
$$k_aAe^{{k_a}t} + k_cBe^{{k_c}t} = k_aCe^{-k_at} + k_c(Ae^{{k_a}t} + Be^{k_ct})$$
Where C is the initial constant of a solution (195). So far I've tried integrating then simplifying (eliminating) both sides of the equation for A, but this is wrong.
$$A=\sqrt{\frac {Ck_a}{k_c}}$$