Notice that the expression on the left side depends only on r, whereas the right expression depends only on t. As a result, this equation is valid in the general case if and only if both sides of the equation are equal to the same constant value. This argument is key in the technique of solving linear partial differential equations by separation of variables. From this observation, we obtain two equations, one for A (r), the other for T (t): ∇ ∇ 2 A A = − − k 2 1 c 2 T d 2 T d t 2 = − − k 2 ,