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^2+xy)dy=(x^2+y^2)dx is (A) logx=log(x-y)+y/x+C (B) logx=2log(x-y)+y/x+C (C) logx=log(x-y)+x/y+C (D) none of these

The solution of xy.log((x)/(y))dx+{y^(2)-x^(2)log((x)/(y))}dy =

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 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

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

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 the differential equation xdy+ydx-sqrt(1-x^(2)y^(2))dx=0 is (A)sin^(-1)(xy)=C-x(B)xy=sin(x+c)(C)log(1-x^(2)y^(2))=x+c(D)y=x sin x+c

If sin^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=log a then (dy)/(dx) is equal to (x^(2)-y^(2))/(x^(2)+y^(2)) (b) (y)/(x) (c) (x)/(y) (d) none of these

If sin^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=log a then (dy)/(dx) is equal to (x^(2)-y^(2))/(x^(2)+y^(2)) (b) (y)/(x) (c) (x)/(y) (d) none of these

The solution of ((dy)/(dx))^(2)+(2x+y)(dy)/(dx)+2xy=0, is (i) (y+x^(2)-c_(1))(x+log y+y^(2)+c_(2))( (ii) (y+x^(2)-c_(1))(x-log y-c_(2))( iii) (y+x^(2)-c_(1))(x+log y-c_(2))( iv) (y+x^(2)-c_(1))(3x+log y-c_(2))