How to solve these two DEQ?

Question

I have given these two equations:

$$ \dot{N}_1(t) = -BN_1(t) + BN_2(t) + AN_2(t) $$ $$ \dot{N}_2(t) = BN_1(t) - BN_2(t) - AN_2(t) $$

where $A,B > 0$ and $N_1 + N_2 = const$, and $N_1(0)=n_1$, $N_2(0)=n_2$.

How to solve these equations?

I have done $N_1+N_2 = C$ and $N_1 = C - N_2$ to get to $ \dot{N}_2(t) = BC - (2B+A)N_2(t) $. But how to solve this homogeneous DEQ?

Answer 1

$$ \dot{N}_2(t) = BC - (2B+A)N_2(t) $$

HINT : Let $N_2(t)=M_2(t)+\frac{BC}{2B+A}$

$$ \dot{M}_2(t) = - (2B+A)M_2(t) $$ Solving this separable ODE is for you.