Black-Scholes equation

The Black-Scholes equation for the value of an option, $V(S,t)$ , on an equity is

$\frac{\partial V}{\partial t}+\frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2}+rS\frac{\partial V}{\partial S} -rV=0$ .

References

Black, F & Scholes, M 1973 The pricing of options and corporate liabilities. Journal of Political Economy 81 637-59