Let `y=y(t)` be a solution to the differential equation `y^(prime)+2t y=t^2,` then `16 ("lim")_(tvecoo)y/t` is_______

If y(t) satisfies the differential equation y'(t)+2y(t)=2e^(-2t),y(0)=2 then y(1) equals

Let x=x(t) and y=y(t) be solutions of the differential equations (dx)/(dt)+ax=0 and (dy)/(dt)+by=0] , respectively, a,b in R .Given that x(0)=2,y(0)=1 and 3y(1)=2x(1) ,the value of "t" ,for which, [x(t)=y(t) ,is :

If x=t^(2) and y=2t then equation of the normal at t=1 is

If y(t) is a solution of (1+t)(dy)/(dt)-ty=1 and y(0)=-1 then y(1) is