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

Show that the differential equation ((x-y)dy)/(dx)=x+2y , is homogeneous and solve it.

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

Solve the differential equation: (dy)/(dx)+y/x=x^2

Solve the differential equation: (x+3y^2)(dy)/(dx)=y

Solve the differential equation : (dy)/(dx)-y/x=2x^2

Solve the differential equation (dy)/(dx) + 2y = x .

Show that the differential equation x^(2)(dy)/(dx) = x^(2)+ xy + y^(2) is homogeneous differential equation. Also find its general solution.

Solve the differential equation: (dy)/(dx)=y^2+2y+2

Solve the differential equation: x (dy)/(dx)+y=3x^(2)-2

Solve the differential equation : log((dy)/(dx))=2x-3y