The solution of `y^2dx+(x^2-xy+y^2)dy=0` is (A) `y=Ce^(tan^-1x)` (B) `y=Ce^(tan^-1y)` (C) `y=Ce^(tan^-1(y/x))` (D) `y=C[tan^-1(y/x)+e^(x^2)+y^2]`

The solution of the differential equation (1+y^2)+(x-e^(tan^-1y))dy/dx=0 is (A) x e^(2 tan^-1y)=e^(tan^-1y)+k (B) (x-2)=k e^(-tan^-1y) (C) x e^(tan^-1y)=e^(2 tan^-1y)+k (D) x e^(tan^-1y)=tan^-1y+k

The solution of (1 + y^(2)) dx = (Tan^(-1) y -x) dy is

The solution of the differential equation (1+y^2)+(x-e^(tan^-1y))dy/dx=0 is (A) x e^(2 tan^-1y)=e^(tan^-1y)+k (B) (x-2)=k e^(-tan^-1y) (C) 2 x e^(tan^-1y)=e^(2 tan^-1y)+k (D) x e^(tan^-1y)=tan^-1y+k

The solution of cos(x+y)dy=dx is (A) y=cos^-1(y/x)+C (B) y=xsec(y/x)+C (C) y=tan((x+y)/2)+C (D) none of these

The solution of cos(x+y)dy=dx is (A) y=cos^-1(y/x)+C (B) y=xsec(y/x)+C (C) y=tan((x+y)/2)+C (D) none of these

The solution of the differential equation (1+y^2)+(xe^(tan^-1)y) (dy)/(dx)=0, is (1) (x-2)=ke^(tan^) -1y) (2) 2xe^(2tan^-1y) =e^(2tan^-1y)+k (3) xe^(tan^-1y)=tan^-1y+k (4) xe^(2tan ^-1y)=e^(tan^-1y)+k

The solution of x^2 dy/dx-xy=1+cos(y/x) is (A) tan(y/(2x))=C-1/(2x^2) (B) sec(y/x)=1+C/y (C) sin(y/x)=C+1/y (D) y^2=(C+x^2) tan(y/x)

The solution of x^2 dy/dx-xy=1+cos(y/x) is (A) tan(y/(2x))=C-1/(2x^2) (B) sec(y/x)=1+C/y (C) sin(y/x)=C+1/y (D) y^2=(C+x^2) tan(y/x)

Solution of differential equation (x^(2)+1)^(2)(dy)/(dx)+2x(x^(2)+1)y=1 is (A) y=(tan^(-1))/(x^(2)+1)+C( B) y=tan^(-1)x+C(C)y(x^(2)+1)=tan^(-1)x+C(D)y(tan^(-1)x)=x^(2)+C