t-e-t? dx + 2x = dt 1 + e-t2 | If it proves that, t X = 2t 212

dx/dt + x cos t = 1/2 sin 2 t

If x= e^(cos2t) and y = e^(sin2t) , then prove that (dy)/(dx) = -(ylogx)/(xlogy) .

if x=e^(t)sin t and y=e^(t)cos t , then prove that (x+y)^(2)(d^(2)y)/dx^(2)=2(xdy/dx-y) .

If x=e^t sin t , y=e^t cos t , t is a parameter , then (d^2y)/(dx^2) at (1,1) is equal to

If x=e^t sin t , y=e^t cos t , t is a parameter , then (d^2y)/(dx^2) at (1,1) is equal to

If x=e^(cos2t) and y=e^(sin2t) , then prove that (dy)/(dx)=(-ylogx)/(x logy) .

If x = e^(t) sin t and y = e^(t) cos t, t is a parameter , then the value of (d^(2) x)/( dy^(2)) + (d^(2) y)/(dx^(2)) at t = 0 , is :

Suppose x=(e^t+e^-t)/2 and y=(e^t-e^-t)/2 are the parametric equations of a curve Find e^t and e^-t in terms of x and y

The equation x = (e ^(t) + e ^(-t))/(2), y = (e ^(t) -e^(-t))/(2), t in R, represents