I have the following PDE
$$ \frac{1}{C(t)}\frac{\mathrm d}{\mathrm d t} \big( C(t) \big)=-\frac{1}{B(S)}(0.5\sigma^2S^2\frac{\mathrm d^2}{\mathrm d S^2}\big (B(S) \big)+rS\frac{\mathrm d}{\mathrm d S}\big( B(S) \big)-rB(S))$$
The text says that since the LHS is function only of t and the RHS is function only of S, both sides must be equal to a constant. I am having a hard time understanding this .
Any help would be appreciated.
Take, for example, a partial derivative $\frac{\partial}{\partial t}$ of both sides. Right hand side gives you zero. Hence, left hand side is equal to a constant as a function of $t$.