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

The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^2+t+1; t in R , is

Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int_(0)^(x)(x-t)f^(')(t)dt y satisfies the differential equation

t in R parametric equation of parabola are x=at^2 and y = 2at .

If x and y are connected parametrically by the equations without eliminating the parameter, find (dy)/(dx) x=4 t, y= (4)/(t)

A curve is represented parametrically by the equations x=e^(t)cost andy=e^(t) sin t, where t is a parameter. Then, If F(t)=int(x+y)dt, then the value of F((pi)/(2))-F(0) is

A curve is represented paramtrically by the equations x=e^(t)cost and y=e^(t)sint where t is a parameter. Then The value of (d^(2)y)/(dx^(2)) at the point where t=0 is

The solution of differential equation xdy(y^(2)e^(xy)+e^(x//y))=ydx(e^(x//y)-y^(2)e^(xy)), is

Find (dy)/(dx) of each of the functions expressed in parametric form: sin x= (2t)/(1 + t^(2)), tan y= (2t)/(1-t^(2)), t in R