The exact solution of partial differential equations, which contains rich information for the equations, is very important for describing the development of various phenomena and thus becomes a research focus of scientific fields such as mathematics, physics, economy and so on. In this paper, the generalized separable solutions for Black-Scholes equation, which is one of most important models arising in financial mathematics, are discussed. By using the conditional Lie-B$\ddot{\rm a}$cklund symmetry and invariant subspace theory, we obtain the conditional Lie-B$\ddot{\rm a}$cklund symmetries, which are similar to Euler equation. The conditional Lie-B$\ddot{\rm a}$cklund symmetries, which are admitted by Black-Scholes, are corresponding to high-order variable coefficient ordinary differential equations. At the same time, all of exact solutions associated to the conditional Lie-B$\ddot{\rm a}$cklund symmetries are performed.
