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

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

Show that the differential equation 2xy(dy)/(dx)=x^(2)+3y^(2) is homogeneousand solve

(dy)/(dx)=(x^(2)-y^(2))/(xy)

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

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

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

Solve (dy)/(dx)=(x^(2)+3y^(2))/(2xy)

Show that the differential equation 2xy (dy)/(dx) = x^2+3y^2 is homogeneousand solve it.

y The differential equation of all circles passing through the origin and having their centres on the x-axis is (1)x^(2)=y^(2)+xy(dy)/(dx) (2) x^(2)=y^(2)+3xy(dy)/(dx)y^(2)=x^(2)+3xy(dy)/(dx)y^(2)=x^(2)-2xy(dy)/(dx)