[" If "y=(cos^(-1)x)^(2)" * whow that "],[(1-x^(2))y_(2)-x_(3)+2=0]

If y=(cos^(-1)x)^(2) , then prove that : (1-x^(2))y_(2)-xy_(1)-2=0 .

(a) If y=cos(msin^(-1)x) prove that (1-x^(2))y_(3)-3xy_(2)+(m^(2)-1)y_(1)=0 (b) Find y'' if x^(4)+y^(4)=16 .

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

If y=(1+cos2x)/(3-2sin2x)," then "(3-2sin2x)^(2)y_(1)=

If cos^(-1)x + cos^(-1)y - cos^(-1) z = 0 , then show that x^(2) + y^(2) + z^(2) - 2xyz = 1

If y=3 cos (log x)+4 sin (log x) Show that x^2 y_2+x y_1+y=0

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)