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 xdy=(2y+2x^4+x^2)dx , is (A) y=x^4+xlogx+C (B) y=x^2+xlogx+C (C) y=x^4+x^2logx+C (D) none of these

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 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 dy/dx=cos(x+y)+sin(x+y) , is given by

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

Solution of, (dy)/(dx)+sin[(x+y)/2]=sin[(x-y)/2] is: (A) ln|tany/2|+2sin(x/2)=c (B) ln|tan(y/4)|+2sin(x/2)=c (C) ln|tany/2|-2sin(x/2)=c (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

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

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 general solution of the differential equation (y dx-x dy)/y=0 is(A) x y = C (B) x=C y^2 (C) y = C x (D) y=C x^2