The differential equation $\frac{dy}{dx} = F(x, y)$ is homogenous differential equation if $F(\lambda x, \lambda y) = F(x, y)$.Examining the above options, (B), (C) and (D) are homogeneous differential equation as below.(B) $F(\lambda x, \lambda y) = \frac{\lambda y}{\lambda x} = \frac{y}{x} = F(x, y)$(C) $F(\lambda x, \lambda y) = \frac{(\lambda x)^2 + (\lambda y^2)}{\lambda x \lambda y} = \frac{\lambda^2 x^2 + \lambda^2 y^2}{\lambda^2 x y} = \frac{x^2 + y^2}{x y} = F(x, y)$(D) $F(\lambda x, \lambda y) = \cos^2\left(\frac{\lambda y}{\lambda x}\right) = \cos^2\left(\frac{y}{x}\right) = F(x, y)$Now we examine (A) as below:(A) $F(\lambda x, \lambda y) = \cos \lambda x - \sin\left(\frac{\lambda y}{\lambda x}\right) = \cos \lambda x - \sin\left(\frac{y}{x}\right) \neq F(x, y)$, so (A) is not a homogeneous differential equation.