`if (dy)/(dx)=(xy^(2)-x^(2)y)/(x^(3))`then the solution is y−Cx=kx 2 y, here k is the const. of integration, find C?

If inte^(-(x^(2))/(2))dx=f(x) and the solution of the differential equation (dy)/(dx)=1+xy is y=ke^((x^(2))/(2))f(x)+Ce^((x^(2))/(2) , then the value of k is equal to (where C is the constant of integration)

y^2dx+(x^2-xy+y^2)dy=0

Find (dy)/(dx)\ if (x^2+y^2)^2=x y

Find (dy)/dx, if (x^2+y^2)^2=xy

Find the solution of (dy)/(dx)=2^(y-x)

The solution of the differential equation (dy)/(dx)=(y^(2)+xlnx)/(2xy) is (where, c is the constant of integration)

The solution of the differential equation (dy)/(dx)=(x-y)/(x+4y) is (where C is the constant of integration)

y(xy+1)dx+x(1+xy+x^(2)y^(2))dy=0

The solution x^2( dy )/( dx) = x^2 + xy + y^2 is :

If (y^(3)-2x^(2)y)dx+(2xy^(2)-x^(3))dy=0, then the value of xysqrt(y^(2)-x^(2)), is