I have solved O.D.E using variable separable but I have no idea how to solve this D.E. using operator method.

$$\dfrac{dT\_h}{dx}+ λ\_h(T\_h-T\_C)=0$$
$$\dfrac{dT\_c}{dx}- λ\_c(T\_h-T\_C)=0$$

The above equations can be written as:
$$(D+λ\_h)T\_h-λ\_hT\_c=0$$
$$(D+λ\_c)T\_c-λ\_cT\_h=0$$
How to proceed further?