The solution of `(1-x^2) dy/dx+2xy-xsqrt(1-x^2)=0`, is (A) `y/((1-x^2))=1/sqrt(1-x^2)+C` (B) `y(1-x^2)=sqrt(1-x^2)+C` (C) `y(1-x^2)^(3/2)=sqrt(1-x^2)+C` (D) none of these

The solution of x sqrt(1+y^(2))dx+y sqrt(1+x^(2))dy=0

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

The differential equation satisfied by sqrt(1+x^2)+sqrt(1+y^2)=k(xsqrt(1+y^2)-ysqrt(1+x^2)), k in R is (A) dy/dx=(1+y^2)/(1+x^2) (B) dy/dx=(1+x^2)/(1+y^2) (C) dy/dx=(1+x^2)(1+y^2) (D) none of these

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

intdx/(sqrt(x)(1+x^2)^(5/4))= (A) (2x)/(1+x^2)^(1/4)+c (B) (2sqrt(x))/(1+x^2)^(1/4)+c (C) (2sqrt(x))/(1+x^2)+c (D) none of these

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), provethat (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

If y=tan^(-1)sqrt((x+1)/(x-1)), then (dy)/(dx) is (-1)/(2|x|sqrt(x^(2)-1)) (b) (-1)/(2x sqrt(x^(2)-1))(1)/(2x sqrt(x^(2)-1))( d) none of these

ysqrt(1-x^(2))+xsqrt(1-y^(2))=1,"show that "(dy)/(dx)=-sqrt((1-y^(2))/(1-x^(2)))