Howdy everyone. I was wondering if someone here could help me out with this test prep question:

If dy/dt = my and m is a nonzero constant, then y could be

(A) 4e^(mty)

(B) 4e^(mt)

(C) e^(mt) + 4

(D) mty + 4

(E) (m/2)y^2 +4

I thought that the first logical step would be antidifferentiation, which, in my mind, produced:

y = tm * (y^2/2)

I then multiplied out and got :

y = (tmy^2)/2

multiplying both sides by two yields :

2y = tmy^2

dividing both sides by y yields:

2 = tmy

Finally, dividing by tm has me believing that y= 2/tm

However, that is not an answer choice, lol.

All help is appreciated!

Have a good one.