Consider two Ordinary Differential Equations $\text{(ODEs)}$:
$\text{P}$: $\frac{d y}{d x}=\frac{x^{4}+3 x^{2} y^{2}+2 y^{4}}{x^{3} y}$
$\mathrm{Q}: \frac{d y}{d x}=\frac{-y^{2}}{x^{2}}$
Which one of the following options is CORRECT?
- $\mathrm{P}$ is a homogeneous $\mathrm{ODE}$ and $\mathrm{Q}$ is an exact $\mathrm{ODE}$.
- $\mathrm{P}$ is a homogeneous $\mathrm{ODE}$ and $\mathrm{Q}$ is not an exact $\mathrm{ODE}$.
- $\mathrm{P}$ is a nonhomogeneous $\mathrm{ODE}$ and $\mathrm{Q}$ is an exact $\mathrm{ODE}$.
- $\mathrm{P}$ is a nonhomogeneous $\mathrm{ODE}$ and $\mathrm{Q}$ is not an exact $\mathrm{ODE}$.