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) 2 x e^(tan^-1y)=e^(2 tan^-1y)+k (D) x e^(tan^-1y)=tan^-1y+k

A differential equation of the form dy/dx+Py=Q is said to be a linear differential equation. Integrating factor of this differential equation is e^(intPdx) and its solution is given by y.e^(int Pdx)=int (Qe^(int Pdx))dx+c . Answer the question:Solution of differential equation (1+y^2)dx+(x-e^(-tan^-1y)dy=0 is (A) y=tan^-1x+c (B) ye^(tan^-1x)=tan^-1x+c (C) xe^(tan^-1y)=tan^-1y+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

(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)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)

The solution of the differential equation (x+y)^2(dy)/(dx)=1 , satisfying the condition y(1)=0 is (A) y+pi/4=tan^(-1)(x+y) (B) y-pi/4=tan^(-1)(x+y) (C) y=tan^(-1)x (D) y=tan^(-1)(ln x)+1

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

The solution of differential equation (1+y^2)+((x-2e^tan^((-1)y))dy)/(dx)=0 is (x-2)=k e^tan^((-1)y) x e^t a n-1y=e^2tan^((-4)y)+k x e^tan^((-1)y)=tan^(-1)y+k x e^2tan^((-1)y)=e^2tan^((-1)y)+k

The solution of the differential equation (1+x^2)(dy)/(dx)+1+y^2=0, is a) tan^(-1)x-tan^(-1)y=tan^(-1)C b) tan^(-1)y-tan^(-1)x=tan^(-1)C c) tan^(-1)y+-tan^(-1)x=tan^(\ )C d) tan^(-1)y+tan^(-1)x=tan^(-1)C

tan^(- 1) (1/(x+y)) +tan^(- 1) (y/(x^2+x y+1)) =cot^(- 1)x