The problem is: Find the continuous solution to the differential equation

dy/dt = 2t+2 if t=<2, or 3t if 2=<t

initial condition y(0) = 2

using that initial condition and the first equation, i solved and got that y(t) = t^2 + 2t + 2

i know that function is continuous, but does it also apply to the 3t or do i need to solve a separate equation? if so, how would i go about doing this?