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

Show that the differential equation [x sin^(2)((y)/(x)) - y]dx+x dy = 0 is homogeneous. Find the particular solution of this differential equation, given that y = (pi)/(4) when x = 1.

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

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

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

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

The differential equation y(dy)/(dx)+x=c represents

The solution of the differential equation : (dy)/(dx)=x+y^2 is :

Solve the differential equation x(dy)/(dx) - y + x cos ((y)/(x)) = 0