If `x=sint` and `y=sin3t`, then the value of k for which `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+k y=0` is

If x=e^(t)sint and y=e^(t)cost , then the value of (x+y)^(2)(d^(2)y)/(dx^(2))-2x(dy)/(dx) is -

If x = sint and y= sin (pt) , then show that (1-x^(2) ) (d^2y)/( dx^2) - x (dy)/( dx) + p^(2) y =0 .

If x=sint,y=sinkt(k ne0 , constant) then show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+k^2y=0 .

if x=2+t^(3),y=3t^(2)" ,then the value of n for which "(((d^(2)y)/(dx^(2))))/((dy)/(dx))^(n) is constant is

If y=sin^(-1)x , show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0 .

If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

If x=sint ,y=sinp t ,"p r o v et h a t" (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx + 4y = 0

If x=sint and y=cos2t , then (dy)/(dx) =

If x=sin t and y=sin pt, prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+p^(2)y=0