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

Let the function x(t) and y(t) satisfy the differential equations (dy)/(dt)+ax=0,(dy)/(dt)+by=0. If x(0)=2,y(0)=1 and (x(1))/(y(1))=(3)/(2), then x(t)=y(t) for t=

If y(t) is the solution of the differential equation (t+1)(dy)/(dt)-ty=1 and y(0)=-1 , then the value of y at t=1 is -

Let y=y(t) be a solution to the differential equation y^(')+2ty=t^(2) , then 16 lim_(t to infty t) y/t is……………….

Let y=y(t) be a solution to the differential equation y'+2ty=t^(2), then 16(lim)_(tvec oo)(y)/(t)

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

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

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

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=f(t) and y=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

Show that the function y=f(x) defined by the parametric equations x=e^(t)sin(t),y=e^(t).cos(t), satisfies the relation y''(x+y)^(2)=2(xy'-y)