If `y=log_e(x/(a+b x))^x` , then `x^3y_2` is
(a) `(x y_1-y)^2`
(b) `(1+y)^2`
(c) `((y-x y_1)/(y_1))^2`
(d) none of these

If y=(log)_e(x/a)^x ,then x^3y_2= (a) (xy_1-y)^2 (b) ((y-x y_1)/(y_1))^2 (c) none of these

If y=(sin^(-1)x)^2,\ then (1-x^2)y_2 is equal to x y_1+2 (b) x y_1-2 (c) x y_1+2 (d) none of these

If y=sin(m\ sin^(-1)x) , then (1-x^2)y_2-x y_1 is equal to m^2y (b) m y (c) -m^2y (d) none of these

If y=(a x+b)/(x^2+c), then (2x y_1+y) y_3=

If (x)/(x-y)=log((a)/(x-y)) then (dy)/(dx) is (a) (x)/(y), (b) 2-(x)/(y), (c) 2, (d) (x-y)/(x)

y=[log(x+sqrt(x^2+1))]^2 then prove that (x^2+1)y_2+x y_1=2

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

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

If the image of the point (x_1, y_1) with respect to the mirror ax+by+c=0 be (x_2 , y_2) then. (a) (x_2-x_1)/a = (a x_1 + b y_1+ c)/(a^(2)+b^(2)) (b) (x_2-x_1)/a = (y_2 - y_1)/b (c) (x_2-x_1)/a = -2 ((a x_1 + b y_1+ c)/(a^(2)+b^(2))) (d) None of these

The solution of the equation dy/dx=x^3y^2+xy is (A) x^2y-2y+1=cye^(-x^2/2) (B) xy^2+2x-y=ce^(-y/2) (C) x^2y-2y+x=cxe^(-y/2) (D) none of these