Linear Differential equation in dx/dy and algorithm to solve them

Homogeneous differential equation and Algorithm to solve them

Solve the differential equation (dx)/(dy)+x=1

Show that the given differential equation is homogeneous and solve each of them.(xy)dy(x+y)dx=0

Show that each of the following differential equations is homogeneous and solve each of them : (x-y)dy=(x+2y)dx .

Show that each of the following differential equations is homogeneous and solve each of them : (x+y)dy-(y-x)dx=0

Show that each of the following differential equations is homogeneous and solve each of them : x^(2)(dy)/(dx)=y(x+y)

Show that each of the following differential equations is homogeneous and solve each of them : (dy)/(dx)= y/x + x/y .

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

Solve the differential equation x*(dy)/(dx)-y=logx .

Solve the differential equation cos x(dy)/(dx)=cos y