Is the prayer of one who did not catch the second prostration with the Imam due to the Imam's quick raising and prostrating valid if he repeats the Rak'ah and performs the prostration of forgetfulness?

It is obligatory for you to sit between the two prostrations and be at ease, then follow the Imam. Your prayer is valid, and there is nothing upon you. However, if you did what you did out of ignorance, your prayer is valid, and you are not required to repeat it.