Solutions of the Black–Scholes PDE

Take $q=0$. (a) Show that $V=S$, $V=e^{rt}$ and $V=S-Ke^{-r(T-t)}$ satisfy (8.18). Interpret each. (b) Find all solutions of the form $V=S^a$ (no time dependence). (c) Using the Greeks of 8.9, verify directly that the call price (8.23) satisfies (8.18).