Try completing the square inside the exponent.
First we define...
(1)
(2)
... and then, remembering that is...
(3)
... from (1), (2) and (3) we derive...
(4)
The (4) is an ordinary first order DE and its general solution is found separating the variables...
(5)
Taking into account the known result we obtain the final result...
(6)
Kind regards