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 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 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

The solution of y(2xy+e^x)dx-e^xdy=0 is (A) x^2+ye^(-x)=C (B) xy^2+e^(-x)=C (C) x/y+e^(-x)/x^2=C (D) x^2+e^x/y=C

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 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

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

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 general solution of the differential equation x^2(1+y^3)dx=y^2(1+x^3)dy is (A) (1+x^2)(1+y^2)=C (B) 1+x^3=C(1+y^3) (C) (x+y)(1+x^2+x^3)=C (D) x(1+y^2)=Cy(1+x^2)

The general solution of the differential equation (d^2y)/dx^2=e^(-3x) is (A) y=9e^(-3x)+C_1x+C_2 (B) y=-3e^(-3x)+C_1x+C_2 (C) y=3e^(-3x)+C_1x+C_2 (D) y=e^(-3x)/9+C_1x+C_2