whats the general solution for dy/dt=2t(2-y)

Question

by integration

Answer 1

dy/(2-y)=2tdt; integrating both sides: -ln(2-y)=t^2+k, where k is a constant.

ln(2-y)=-t^2-k, 2-y=e-(t^2)*e^-k=ae^-t^2, where a is a constant related to k.

Therefore y=2-ae^-t^2.