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 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 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)+(y)/(x)=(1)/((1+log x+log y)^(2)) 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

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

If y=log_e(x/(a+b x))^x , then x^3y_2 is (a) (x y_1-y)^2 (b) (1+y)^2 (c) ((y-x y_1)/(y_1))^2 (d) none of these

The factors of x^3-x^2y-x y^2+y^3 are (a (x+y)(x^2-x y+y^2) (b) (x+y)(x^2+x y+y^2) (c) (x+y)^2(x-y) (d) (x-y)^2(x+y)

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3- (log)_3 2 (c) log(3/2) (d) none of these

The solution of x^2+y^2(dy)/(dx)=4 is a. x^2+y^2=12 x+C b. x^2+y^2=3x+C c. x^3+y^3=3x+C d. x^3+y^3=12 x+C