White to move and mate in 2 moves (XXI)

Is this the solution?

No because of two reasons.

1) What you are supposed to find is mate in 2 not 3

2) 2. Re1+ is illegal because it leaves whites king in check by the black queen.

first situation:

1. Kc7, Qh2+ 2. Re5#

second situation:

1. Kc7 Nxd2 2.Nc1 #

third situation:

1. Kc7  Bd6+ 2. Qxd6#

fourth situation:

1. Kc7  a move which I didn't wrote it up 2. Qa6# 

it was hard. tell me if i made a mistake please. Anyway, nice position.

congratulation you found it

thanks, but you were faster

and i was helped so...

And 1. .. Bxd2 2. Nc5#

Note that both mates were already present in the diagram (assuming black on move). That makes them less valuable for the composition than the new mates resulting from the white key move (3. Qa6#, 3.Re5# and 3.Rd4#).