Which of the following equation has \(y=x\) as one of its particular solution?

\(\frac{d^2 y}{dx^2}-x^2\frac{dy}{dx}+xy=x\) \(\frac{d^2 y}{dx^2}+x\frac{dy}{dx}+xy=x\) \(\frac{d^2 y}{dx^2}-x^2\frac{dy}{dx}+xy=0\) \(\frac{d^2 y}{dx^2}+x\frac{dy}{dx}+xy=0\)

\(\frac{d^2 y}{dx^2}-x^2\frac{dy}{dx}+xy=0\)

Substitute and verify