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Basically, I am confused by one question in a practice paper in which the equation is given as follows:

dy/dx = e^-2y

and I know the general solution is equal to : y = -0.5e^-2y + C

which would make sense if it was direct integration however it seems to me it is in fact separable integration as there is a lone function of y. Below is a picture of my attempt at a solution through separable integration and would appreciate if anyone has any input? Am I wrong in thinking it's seperable?

dy/dx = e^-2y

and I know the general solution is equal to : y = -0.5e^-2y + C

which would make sense if it was direct integration however it seems to me it is in fact separable integration as there is a lone function of y. Below is a picture of my attempt at a solution through separable integration and would appreciate if anyone has any input? Am I wrong in thinking it's seperable?