solution of homogeneous differential equation

Homogeneous differential equation || Reducible to homogeneous differential equation linear differential equation

Homogeneous differential equation || reducible to homogeneous differential equation linear

Which of the following is a homogeneous differential equation ?

Consider the differential equation (dy)/(dx)=(y^(3))/(2(xy^(2)-x^(2))) Statement 1 The substitution z=y^(2) transforms the above equation into first order homogeneous differential equation Statement 2: The solution of this differential equation is y^(2)e^((-y^(2))/(x))=C

Show that the differential equation 2ye^((pi)/(y))dx+(y-2xe^(xy))dy=0 is homogeneous.Find the particular solution of this differential equation,given that x=0 when y=1.

Show that the differential equation x(dy)/(dx)sin(y/x)+x-ysin(y/x)=0 is homogenous. Find the particular solution of this differential equation, given that x=1 when y=pi/2 .

Show that y^(2)dx + (xy + x^(2))dy = 0 is a homogeneous differential equation. Also find its general solution.

The substituting y=vx reduces the homogeneous differential equation (dy)/(dx)=(y)/(x)+tan.(y)/(x) to the form