In the Black-Scholes framework when the underlying does not pay dividends,

(1). Write down the Black-Scholes formula for the price of a European Put at time t.

(2). Based on the modeling of the price of the underlying stock in the BlackScholes framework, please derive the stochastic differential equation followed by the instantaneous dollar return of the European Put over time t to t +dt , dp_t =?

You need to show clear derivation steps.