Prove that the equation `x62(dy)/(dx)=x^2-2y^2+xy` is a homogenous differential equation

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

Verify that the function y = e^(2x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0

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

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

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.

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.

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

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

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