If `y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx)` is equal to (a)`x+y` (b) `1+x y` (c) `1-x y` (d) `x y-2`

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

If y=sin^(-1)x/sqrt(1-x^(2)) show that (1-x^(2))y_(2)-3xy_(1)-y=0 .

If y = (sin^(-1) x)/(sqrt(1-x^2)) show that (1-x^2) y_2 - 3xy_1 - y =0

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to

(y-e^(sin^(-1)x))(dy)/(dx)+sqrt(1-x^(2))=0.

If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2-y^2)/(x^2+y^2) (d) y/x

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

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

Given y=(5x)/(3sqrt((1-x)^2 ))+sin^2(2x+1), (dy)/(dx)

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)