Black-Scholes equation

1. Verify that S(t)e-d(T -t)N (d1) satisfies the Black-Scholes equation.
2. Verify that e-r(T -t)N (d2) satisfies the Black-Scholes equation.
3. Use the answers to the previous two problems to verify that the Black-Scholes formula, equation (12.1), satisfies the Black-Scholes equation. Verify that the boundary condition V [S(T ), T ] = max[0, S(T ) – K] is satisfied.