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

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

(i) if x=sint , y= sinpt , then show that (1-x^2) d^2 y/dx^2 - x dy/dx +p^2 y =0 . Br Determine the differentials of z=cos 2t -2 cot t .

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=cos theta and y=sin 5 theta , then prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+25y=0

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

If y=e^(x)sinx , then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 ,

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 y=(sin^(-1)x)/(sqrt(1-x^(2))) , the prove that (1-x^(2))(d^(2)y)/(dx^(2))-3x(dy)/(dx)-y=0 .