Before revision:  Also, to generalize, the option price is derived for the case of  a geometric Brownian motion with the time-dependent drift and volatility  .
After revision:  Also, to generalize, the option price is derived for the case of a geometric Brownian motion with the time-dependent drift and volatility which is important to use the solutions in real life applications. The formulas are derived for the drift that may include non-negative or negative "dividend" yield. The latter case results in a new solution type that has not been studied in the literature. Several typographical errors in the formula for the holder-extendible put, typically repeated in textbooks and software, are corrected .