While you may THINK that is the only answer, is it true that y==0 is also a solution?
How about the constant value of sqrt(2)? -sqrt(2)?
So is it vaguely possible that your hand calculated solution is not a complete one?
Next, consider that any expression can be writtten in different, but valid ways. Consider the expression:
exp(C + x)
where C is some unknown constant. Can that also be written as
D*exp(x)
where D is some equally unknown constant?
Since you did not provide initial values of any sort to dsolve, it produces a valid solution. The solution may not look exactly like yours, but it is still a valid solution, and in fact, a more complete solution than what you found.
